自立学習×個別指導

NextStage

学習塾 ネクストステージ

埼玉県川越市大字砂935-6

新河岸駅下車徒歩2分

電話 049-265-8994

FAX 049-265-8640

2017/06/13

月刊ネクスト6月号「入試問題に挑戦」の答え

3桁の整数ABCを4分の3倍すると3桁の整数BCAになり、さらにBCAを4分の3倍するとCABになります。このような3桁の整数を2つ答えなさい。

(2017年度灘中1日目入試より)


 

【解法】

 

式に表してみます。

BCAABC×3/4

CABBCA×3/4

CAB=ABC×9/16

 

ここから

BCAは4の倍数…①

ABCは16の倍数…②

CABは9の倍数 …③

であることがわかりますね。

 

また、9の倍数の条件は

「各位の数の和が9の倍数」なので、

①は C+A+B=(9の倍数) となり、

②においても A+B+C=(9の倍数) が成り立ち、

ABCは9の倍数かつ16の倍数であることがわかります。

 

9と16の最小公倍数は144なので、

ABCは144の倍数です。

 

3けたの144の倍数を全部書き出して調べます。(→は4分の3倍の計算)

144 … ダメ(ABB)

288 … ダメ(ABB)

432 → 324 → 243

576 → 432 …ダメ(ABC→EFG)

720 … ダメ(C=0なのでCABは存在しない)

864 → 648 → 486

 

よって、432と864の2つが答えとなります。

 

答えが2つというヒントがあったので、割とスムーズに解ける問題でした。

ケアレスミスの要素を排除して、基本的な概念の理解と論理的思考を試そうとする良問ですね。

こういう問題を解くと「スカッと」しますね。

 

 

学習塾NextStage ( ネクストステージ )
■営業時間
平日13:00~21:30
土曜10:00~21:30
日曜 不定期
■住所
埼玉県川越市大字砂935-6
■電話
049-265-8994            
2017/06/13

1学期中間試験「特別企画」…の結果

みなさん、こんにちは。

 

塾生はみんな知っていたかと思いますが、もしかしたら保護者の方は初耳かもしれません。

 

実は、今回の定期試験に向け、塾の特別企画として、「成績アップキャンペーン」を実施していました。

 

・学年順位10以上アップ

・学年順位10位以内

 

を目標に掲げて、達成して人には心ばかりのプレゼントを贈呈(*^。^*)…といった内容です。

 


 

 

定期試験特別企画_塾_ネクストステージ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

そもそも、このキャンペーンを実施した理由は、

「塾生から闘志が感じられない!」

…そんな状況にあったからです。

 


 

 

さて、結果は…

(6月13日時点判明分です。判明次第、追加訂正を行います。)

 

●中学1年生が大健闘!

 学年順位10番以内が3名(^_-)-☆

(学年順位11番もいましたが、表彰の対象外…NextStageに情けはありません。思いっきり悔しがってください。そして次回頑張りましょう!)

中学1年生にとって勝負はここからです。期末試験…9教科になるし、内容が難しくなるし…ハードルがたくさんですね ( ;∀;) 楽しみながら頑張りましょう!

 

●中学3年生…受験生として目覚める!?

この時期、保護者の方と話していると、「受験生としての自覚がないんですよねぇ…」みたいな会話になります。

 

まぁ、この時期は部活もまだあるので、気持ちの切り替えが難しいですね。

 

少し話が脱線しますが、保護者の方に意識しておいてほしいのが、いくら中学3年生と言えども、ほとんどの生徒が「初めての受験」だということ…。つまり、何にもわかっていないのです。だからこそ大人が教えてあげて、サポートをしてあげる必要があります。

‥‥‥‥話が長くなりそうなので、この話題はまた今度にしましょう。

 

で、今回の定期試験…私が思っていたより自覚を持って勉強してくれていました。すばらしい(^◇^)

 

順位が10位以上あがった生徒は2人、学年10位以内が1人(*^。^*)

今回のテストで、初めて5科450点以上を超えた塾生もいました。「やればできる」ことに気づけたでしょう!

 

 

 


 

 

 

 

‥‥‥‥‥‥あれぇ~……………。中学2年生は‥‥‥‥‥‥。

 

‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥根性から叩き直しですね(#^.^#)

 


 

 

 

学習塾NextStage ( ネクストステージ )
■営業時間
平日13:00~21:30
土曜10:00~21:30
日曜 不定期
■住所
埼玉県川越市大字砂935-6
■電話
049-265-8994            
2017/04/03

ディズニーランド…!?

春休みに子どもたちと会話をしていると…

 

「ディズニーランド行ってきたよ~!」

 

「明後日、ディズニーランド行くよ~!」

 

そんな会話ばっかり。

 

 

 

NextStageの塾生はディズニーランドより勉強の方が好きかと思っていたのに…。

 

 

 

…くっそー!

 

 

 

うらやましい…。

 

 

 

こうなったら気分だけでも行った気になるしかない。

 

 

 

お土産でもらった耳をつけて…(ゴソゴソ)

 

 

 

スマホで自撮り…(カチャッ)

(慣れていないのでうまく撮れないよ~…)

 

 

 

うん…、これだけだとかなりイタイ写真になったので、

 

 

 

画像編集ソフトで適当にデコって…(カチカチ)

 

 

 

できた!

 

 

 

ついにできました!

 

 

 

 

完成品です!

 

 

Nextland_640×480

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

「現実と勉強の国…Nextlandへようこそ!」

 

学習塾NextStage ( ネクストステージ )
■営業時間
平日13:00~21:30
土曜10:00~21:30
日曜 不定期
■住所
埼玉県川越市大字砂935-6
■電話
049-265-8994            
2017/03/29

センチュリーパズル!?

みなさん、こんにちは!

 

今年の春は、なんとなく「のんびり」な学習塾NextStageです。

 

新学年に向けて、計画的に学習の貯蓄をしてほしいところですが……実際に始まってみて痛い目を見ないとわからないものですね…。夏休みや冬休みは皆さん一生懸命勉強しますが、春休みは勉強への意識の差が一番でやすい時期かも知れません。受験生として頑張り始める人、まだまだ大丈夫と考えてのんびりしている人、中学校や高校への準備を進める人、最後のチャンスとばかりに遊び惚ける人……。勉強だけがすべてではありませんが、先を見据えて行動するようにしましょう!


b20164402806eb8d3e6f1fcf62b679b6_s

 

 

 

 

さて先日、私立中学校へ進学する生徒から
「算数の自由研究何をすれば良いの??」と聞かれたのですが、すぐに思い浮かばなかったのでパソコンで調べていると、「センチュリーパズル」の文字が…。

 

なんとなくカッコよかったので、さらに調べてみると、小町算のなかまであることがわかりました。
小町算は
1□2□3□4□5□6□7□8□9=100
を満たすように□に記号(+-÷×)を入れなさいよ!という問題です。

 

一度ぐらいみたことあるのではないでしょうか。
それに対してセンチュリーパズルは1~9までの数字を1つずつ使って
100=□+△/〇(帯分数)のかたちで表しなさい!という問題です。

 

まぁ、面倒くさい!

 

答えは、検索するとすぐに出てくるのであまり興味は湧かなかったのですが、
「100以外の数も同様に表せるの?」という疑問が…。
検索しても出てこなかったで自分で計算してみました。

 

考察から先にいうと、なかなか面白い結果になりました。まだ詳しく考察できてませんが、以下のようなことはすぐに気づけると思います。
・1以外の解はすべて存在する。
・60のように切りの良い数よりも、59のような素数の方が解がたくさんある。
・素数だからと解がたくさんあるとは限らない。
・おそらく1~9876543210まで調べると、解の個数の分布に規則がありそう。

 

それでは答えです。

 

 

答え一覧(1~100)

1 = 存在しない
————–
2 = 0 + ( 13458 / 6729 )
2 = 0 + ( 13584 / 6792 )
2 = 0 + ( 13854 / 6927 )
2 = 0 + ( 14538 / 7269 )
2 = 0 + ( 14586 / 7293 )
2 = 0 + ( 14658 / 7329 )
2 = 0 + ( 15384 / 7692 )
2 = 0 + ( 15846 / 7923 )
2 = 0 + ( 15864 / 7932 )
2 = 0 + ( 18534 / 9267 )
2 = 0 + ( 18546 / 9273 )
2 = 0 + ( 18654 / 9327 )
————–
3 = 0 + ( 17469 / 5823 )
3 = 0 + ( 17496 / 5832 )
————–
4 = 0 + ( 15768 / 3942 )
4 = 0 + ( 17568 / 4392 )
4 = 0 + ( 23184 / 5796 )
4 = 0 + ( 31824 / 7956 )
————–
5 = 0 + ( 13485 / 2697 )
5 = 0 + ( 13845 / 2769 )
5 = 0 + ( 14685 / 2937 )
5 = 0 + ( 14835 / 2967 )
5 = 0 + ( 14865 / 2973 )
5 = 0 + ( 16485 / 3297 )
5 = 0 + ( 18645 / 3729 )
5 = 0 + ( 31485 / 6297 )
5 = 0 + ( 38145 / 7629 )
5 = 0 + ( 46185 / 9237 )
5 = 0 + ( 48135 / 9627 )
5 = 0 + ( 48615 / 9723 )
5 = 1 + ( 30592 / 7648 )
5 = 1 + ( 35704 / 8926 )
5 = 2 + ( 10974 / 3658 )
5 = 2 + ( 17049 / 5683 )
5 = 2 + ( 19074 / 6358 )
5 = 3 + ( 10972 / 5486 )
5 = 3 + ( 12970 / 6485 )
5 = 3 + ( 17092 / 8546 )
5 = 3 + ( 17290 / 8645 )
————–
6 = 0 + ( 17658 / 2943 )
6 = 0 + ( 27918 / 4653 )
6 = 0 + ( 34182 / 5697 )
6 = 2 + ( 14780 / 3695 )
6 = 2 + ( 34076 / 8519 )
6 = 2 + ( 36740 / 9185 )
6 = 3 + ( 17082 / 5694 )
6 = 3 + ( 20457 / 6819 )
6 = 3 + ( 20754 / 6918 )
6 = 3 + ( 24507 / 8169 )
6 = 3 + ( 27504 / 9168 )
————–
7 = 0 + ( 16758 / 2394 )
7 = 0 + ( 18459 / 2637 )
7 = 0 + ( 31689 / 4527 )
7 = 0 + ( 36918 / 5274 )
7 = 0 + ( 37926 / 5418 )
7 = 0 + ( 41832 / 5976 )
7 = 0 + ( 53298 / 7614 )
7 = 1 + ( 56082 / 9347 )
7 = 3 + ( 20784 / 5196 )
7 = 3 + ( 24780 / 6195 )
7 = 3 + ( 27804 / 6951 )
7 = 4 + ( 20517 / 6839 )
7 = 4 + ( 25107 / 8369 )
————–
8 = 0 + ( 25496 / 3187 )
8 = 0 + ( 36712 / 4589 )
8 = 0 + ( 36728 / 4591 )
8 = 0 + ( 37512 / 4689 )
8 = 0 + ( 37528 / 4691 )
8 = 0 + ( 38152 / 4769 )
8 = 0 + ( 41896 / 5237 )
8 = 0 + ( 42968 / 5371 )
8 = 0 + ( 46312 / 5789 )
8 = 0 + ( 46328 / 5791 )
8 = 0 + ( 46712 / 5839 )
8 = 0 + ( 47136 / 5892 )
8 = 0 + ( 47328 / 5916 )
8 = 0 + ( 47368 / 5921 )
8 = 0 + ( 51832 / 6479 )
8 = 0 + ( 53928 / 6741 )
8 = 0 + ( 54312 / 6789 )
8 = 0 + ( 54328 / 6791 )
8 = 0 + ( 54712 / 6839 )
8 = 0 + ( 56984 / 7123 )
8 = 0 + ( 58496 / 7312 )
8 = 0 + ( 58912 / 7364 )
8 = 0 + ( 59328 / 7416 )
8 = 0 + ( 59368 / 7421 )
8 = 0 + ( 63152 / 7894 )
8 = 0 + ( 63528 / 7941 )
8 = 0 + ( 65392 / 8174 )
8 = 0 + ( 65432 / 8179 )
8 = 0 + ( 67152 / 8394 )
8 = 0 + ( 67352 / 8419 )
8 = 0 + ( 67512 / 8439 )
8 = 0 + ( 71456 / 8932 )
8 = 0 + ( 71536 / 8942 )
8 = 0 + ( 71624 / 8953 )
8 = 0 + ( 71632 / 8954 )
8 = 0 + ( 73248 / 9156 )
8 = 0 + ( 73264 / 9158 )
8 = 0 + ( 73456 / 9182 )
8 = 0 + ( 74528 / 9316 )
8 = 0 + ( 74568 / 9321 )
8 = 0 + ( 74816 / 9352 )
8 = 0 + ( 75328 / 9416 )
8 = 0 + ( 75368 / 9421 )
8 = 0 + ( 76184 / 9523 )
8 = 0 + ( 76248 / 9531 )
8 = 0 + ( 76328 / 9541 )
8 = 1 + ( 32956 / 4708 )
8 = 1 + ( 56329 / 8047 )
8 = 1 + ( 57463 / 8209 )
8 = 1 + ( 63574 / 9082 )
8 = 2 + ( 41370 / 6895 )
8 = 3 + ( 14780 / 2956 )
8 = 3 + ( 45860 / 9172 )
8 = 3 + ( 46085 / 9217 )
8 = 3 + ( 47810 / 9562 )
8 = 3 + ( 48560 / 9712 )
8 = 3 + ( 48605 / 9721 )
8 = 4 + ( 15628 / 3907 )
8 = 4 + ( 28156 / 7039 )
8 = 4 + ( 36508 / 9127 )
8 = 5 + ( 13827 / 4609 )
8 = 5 + ( 27138 / 9046 )
8 = 5 + ( 27408 / 9136 )
8 = 6 + ( 10478 / 5239 )
8 = 6 + ( 10784 / 5392 )
8 = 6 + ( 18470 / 9235 )
8 = 6 + ( 18704 / 9352 )
————–
9 = 0 + ( 57429 / 6381 )
9 = 0 + ( 58239 / 6471 )
9 = 0 + ( 75249 / 8361 )
9 = 2 + ( 51863 / 7409 )
9 = 2 + ( 63518 / 9074 )
9 = 3 + ( 28170 / 4695 )
9 = 5 + ( 28364 / 7091 )
9 = 5 + ( 28436 / 7109 )
9 = 5 + ( 36284 / 9071 )
9 = 5 + ( 36428 / 9107 )
9 = 6 + ( 10782 / 3594 )
9 = 6 + ( 17802 / 5934 )
————–
10 = 1 + ( 85203 / 9467 )
10 = 6 + ( 19032 / 4758 )
10 = 6 + ( 30192 / 7548 )
10 = 6 + ( 37140 / 9285 )
————–
11 = 2 + ( 75069 / 8341 )
11 = 4 + ( 19306 / 2758 )
11 = 6 + ( 17290 / 3458 )
11 = 6 + ( 17920 / 3584 )
11 = 6 + ( 19270 / 3854 )
11 = 6 + ( 20935 / 4187 )
11 = 6 + ( 21790 / 4358 )
11 = 6 + ( 23590 / 4718 )
11 = 6 + ( 23905 / 4781 )
11 = 6 + ( 27190 / 5438 )
11 = 6 + ( 29170 / 5834 )
11 = 6 + ( 35920 / 7184 )
11 = 6 + ( 39205 / 7841 )
11 = 7 + ( 10384 / 2596 )
11 = 7 + ( 38104 / 9526 )
11 = 9 + ( 10476 / 5238 )
11 = 9 + ( 10728 / 5364 )
11 = 9 + ( 10764 / 5382 )
11 = 9 + ( 10872 / 5436 )
11 = 9 + ( 12708 / 6354 )
11 = 9 + ( 12870 / 6435 )
11 = 9 + ( 13704 / 6852 )
11 = 9 + ( 16470 / 8235 )
11 = 9 + ( 16704 / 8352 )
11 = 9 + ( 17046 / 8523 )
11 = 9 + ( 17064 / 8532 )
11 = 9 + ( 17304 / 8652 )
————–
12 = 0 + ( 45792 / 3816 )
12 = 0 + ( 73548 / 6129 )
12 = 0 + ( 89532 / 7461 )
12 = 0 + ( 91584 / 7632 )
12 = 3 + ( 47601 / 5289 )
12 = 3 + ( 54729 / 6081 )
12 = 3 + ( 54972 / 6108 )
12 = 3 + ( 72549 / 8061 )
12 = 3 + ( 72954 / 8106 )
12 = 5 + ( 28637 / 4091 )
12 = 5 + ( 28763 / 4109 )
12 = 5 + ( 63287 / 9041 )
12 = 5 + ( 63728 / 9104 )
12 = 5 + ( 68201 / 9743 )
12 = 6 + ( 34902 / 5817 )
12 = 8 + ( 10376 / 2594 )
12 = 8 + ( 15704 / 3926 )
12 = 8 + ( 17036 / 4259 )
12 = 8 + ( 19052 / 4763 )
12 = 8 + ( 37016 / 9254 )
12 = 9 + ( 10746 / 3582 )
————–
13 = 0 + ( 67392 / 5184 )
13 = 0 + ( 81549 / 6273 )
13 = 0 + ( 94653 / 7281 )
13 = 4 + ( 82503 / 9167 )
13 = 6 + ( 32109 / 4587 )
13 = 7 + ( 50214 / 8369 )
13 = 9 + ( 10548 / 2637 )
13 = 9 + ( 14508 / 3627 )
13 = 9 + ( 15048 / 3762 )
13 = 9 + ( 20736 / 5184 )
13 = 9 + ( 30168 / 7542 )
————–
14 = 0 + ( 25746 / 1839 )
14 = 0 + ( 27384 / 1956 )
14 = 0 + ( 41538 / 2967 )
14 = 0 + ( 46158 / 3297 )
14 = 0 + ( 51492 / 3678 )
14 = 0 + ( 54768 / 3912 )
14 = 0 + ( 61572 / 4398 )
14 = 0 + ( 65982 / 4713 )
14 = 1 + ( 35074 / 2698 )
14 = 2 + ( 50376 / 4198 )
14 = 2 + ( 86340 / 7195 )
14 = 5 + ( 36729 / 4081 )
14 = 5 + ( 36972 / 4108 )
14 = 5 + ( 72369 / 8041 )
14 = 5 + ( 72936 / 8104 )
14 = 7 + ( 21658 / 3094 )
14 = 7 + ( 28651 / 4093 )
14 = 7 + ( 65128 / 9304 )
14 = 7 + ( 65821 / 9403 )
14 = 9 + ( 17280 / 3456 )
14 = 9 + ( 17640 / 3528 )
14 = 9 + ( 17820 / 3564 )
14 = 9 + ( 18270 / 3654 )
14 = 9 + ( 20685 / 4137 )
14 = 9 + ( 20835 / 4167 )
14 = 9 + ( 20865 / 4173 )
14 = 9 + ( 21780 / 4356 )
14 = 9 + ( 23085 / 4617 )
14 = 9 + ( 23580 / 4716 )
14 = 9 + ( 23805 / 4761 )
14 = 9 + ( 27180 / 5436 )
14 = 9 + ( 28170 / 5634 )
14 = 9 + ( 32085 / 6417 )
14 = 9 + ( 35640 / 7128 )
14 = 9 + ( 35820 / 7164 )
14 = 9 + ( 36405 / 7281 )
14 = 9 + ( 38205 / 7641 )
14 = 9 + ( 40635 / 8127 )
14 = 9 + ( 41760 / 8352 )
14 = 9 + ( 43560 / 8712 )
14 = 9 + ( 43605 / 8721 )
14 = 12 + ( 6970 / 3485 )
14 = 12 + ( 7096 / 3548 )
14 = 12 + ( 7690 / 3845 )
14 = 12 + ( 9076 / 4538 )
14 = 12 + ( 9370 / 4685 )
14 = 12 + ( 9670 / 4835 )
14 = 12 + ( 9706 / 4853 )
14 = 12 + ( 9730 / 4865 )
————–
15 = 0 + ( 27945 / 1863 )
15 = 0 + ( 92745 / 6183 )
15 = 2 + ( 70148 / 5396 )
15 = 3 + ( 81504 / 6792 )
15 = 8 + ( 36029 / 5147 )
15 = 9 + ( 21870 / 3645 )
15 = 9 + ( 27810 / 4635 )
15 = 9 + ( 38502 / 6417 )
————–
16 = 0 + ( 45936 / 2871 )
16 = 0 + ( 73296 / 4581 )
16 = 0 + ( 98352 / 6147 )
16 = 1 + ( 67980 / 4532 )
16 = 1 + ( 79860 / 5324 )
16 = 1 + ( 94305 / 6287 )
16 = 3 + ( 20748 / 1596 )
16 = 3 + ( 62517 / 4809 )
16 = 4 + ( 91032 / 7586 )
16 = 4 + ( 97620 / 8135 )
16 = 9 + ( 21546 / 3078 )
16 = 9 + ( 32067 / 4581 )
16 = 9 + ( 40761 / 5823 )
16 = 9 + ( 50841 / 7263 )
16 = 9 + ( 54621 / 7803 )
————–
17 = 0 + ( 26843 / 1579 )
17 = 0 + ( 28543 / 1679 )
17 = 0 + ( 29546 / 1738 )
17 = 0 + ( 36958 / 2174 )
17 = 0 + ( 45713 / 2689 )
17 = 0 + ( 45781 / 2693 )
17 = 0 + ( 54689 / 3217 )
17 = 0 + ( 59126 / 3478 )
17 = 0 + ( 64957 / 3821 )
17 = 0 + ( 65297 / 3841 )
17 = 0 + ( 67184 / 3952 )
17 = 0 + ( 67218 / 3954 )
17 = 0 + ( 76823 / 4519 )
17 = 0 + ( 76891 / 4523 )
17 = 0 + ( 78132 / 4596 )
17 = 0 + ( 78523 / 4619 )
17 = 0 + ( 78591 / 4623 )
17 = 0 + ( 81532 / 4796 )
17 = 0 + ( 83572 / 4916 )
17 = 0 + ( 83657 / 4921 )
17 = 0 + ( 89437 / 5261 )
17 = 0 + ( 89471 / 5263 )
17 = 0 + ( 89641 / 5273 )
17 = 0 + ( 91426 / 5378 )
17 = 0 + ( 92837 / 5461 )
17 = 0 + ( 92871 / 5463 )
17 = 0 + ( 93126 / 5478 )
17 = 1 + ( 39760 / 2485 )
17 = 1 + ( 65392 / 4087 )
17 = 2 + ( 46185 / 3079 )
17 = 2 + ( 58740 / 3916 )
17 = 3 + ( 25046 / 1789 )
17 = 3 + ( 57806 / 4129 )
17 = 3 + ( 60158 / 4297 )
17 = 3 + ( 65912 / 4708 )
17 = 3 + ( 71246 / 5089 )
17 = 3 + ( 72086 / 5149 )
17 = 3 + ( 85274 / 6091 )
17 = 3 + ( 94052 / 6718 )
17 = 4 + ( 36517 / 2809 )
17 = 4 + ( 68107 / 5239 )
17 = 4 + ( 93028 / 7156 )
17 = 5 + ( 73128 / 6094 )
17 = 5 + ( 86304 / 7192 )
17 = 8 + ( 27549 / 3061 )
17 = 8 + ( 27954 / 3106 )
17 = 8 + ( 54279 / 6031 )
17 = 8 + ( 54927 / 6103 )
17 = 9 + ( 16584 / 2073 )
17 = 9 + ( 18456 / 2307 )
17 = 9 + ( 18760 / 2345 )
17 = 9 + ( 24568 / 3071 )
17 = 9 + ( 24856 / 3107 )
17 = 9 + ( 25408 / 3176 )
17 = 9 + ( 27608 / 3451 )
17 = 9 + ( 32568 / 4071 )
17 = 9 + ( 32856 / 4107 )
17 = 9 + ( 37208 / 4651 )
17 = 9 + ( 38016 / 4752 )
17 = 9 + ( 38120 / 4765 )
17 = 9 + ( 50184 / 6273 )
17 = 9 + ( 50728 / 6341 )
17 = 9 + ( 51024 / 6378 )
17 = 9 + ( 51072 / 6384 )
17 = 9 + ( 56184 / 7023 )
17 = 9 + ( 56248 / 7031 )
17 = 9 + ( 56328 / 7041 )
17 = 9 + ( 56824 / 7103 )
17 = 9 + ( 56832 / 7104 )
17 = 9 + ( 58104 / 7263 )
17 = 9 + ( 58416 / 7302 )
17 = 9 + ( 60184 / 7523 )
17 = 9 + ( 60248 / 7531 )
17 = 9 + ( 60328 / 7541 )
17 = 9 + ( 62504 / 7813 )
17 = 9 + ( 65072 / 8134 )
17 = 9 + ( 65704 / 8213 )
17 = 9 + ( 67320 / 8415 )
————–
18 = 0 + ( 28674 / 1593 )
18 = 2 + ( 50864 / 3179 )
18 = 3 + ( 25470 / 1698 )
18 = 3 + ( 40185 / 2679 )
18 = 5 + ( 36491 / 2807 )
18 = 5 + ( 80249 / 6173 )
18 = 5 + ( 83291 / 6407 )
18 = 5 + ( 91364 / 7028 )
18 = 5 + ( 91832 / 7064 )
18 = 6 + ( 71208 / 5934 )
————–
19 = 0 + ( 51984 / 2736 )
19 = 0 + ( 81567 / 4293 )
19 = 1 + ( 50364 / 2798 )
19 = 1 + ( 53604 / 2978 )
19 = 3 + ( 81264 / 5079 )
19 = 3 + ( 82704 / 5169 )
19 = 4 + ( 20685 / 1379 )
19 = 4 + ( 23790 / 1586 )
19 = 4 + ( 26085 / 1739 )
19 = 4 + ( 76980 / 5132 )
19 = 4 + ( 79680 / 5312 )
19 = 4 + ( 92370 / 6158 )
19 = 6 + ( 95082 / 7314 )
19 = 15 + ( 8376 / 2094 )
————–
20 = 1 + ( 53086 / 2794 )
20 = 2 + ( 35604 / 1978 )
20 = 2 + ( 86310 / 4795 )
20 = 5 + ( 73680 / 4912 )
20 = 6 + ( 20398 / 1457 )
20 = 6 + ( 54712 / 3908 )
20 = 6 + ( 58702 / 4193 )
20 = 6 + ( 59038 / 4217 )
20 = 7 + ( 51064 / 3928 )
20 = 7 + ( 52819 / 4063 )
20 = 7 + ( 69082 / 5314 )
20 = 7 + ( 81952 / 6304 )
20 = 18 + ( 7092 / 3546 )
20 = 18 + ( 7290 / 3645 )
20 = 18 + ( 9072 / 4536 )
20 = 18 + ( 9270 / 4635 )
————–
21 = 2 + ( 58976 / 3104 )
21 = 2 + ( 76589 / 4031 )
21 = 2 + ( 98306 / 5174 )
21 = 3 + ( 91476 / 5082 )
21 = 5 + ( 28304 / 1769 )
21 = 5 + ( 68912 / 4307 )
21 = 6 + ( 41085 / 2739 )
21 = 6 + ( 72135 / 4809 )
21 = 8 + ( 40976 / 3152 )
21 = 8 + ( 52793 / 4061 )
21 = 8 + ( 53261 / 4097 )
21 = 8 + ( 79352 / 6104 )
————–
22 = 0 + ( 51678 / 2349 )
22 = 3 + ( 80769 / 4251 )
22 = 4 + ( 38970 / 2165 )
22 = 4 + ( 71208 / 3956 )
22 = 6 + ( 48912 / 3057 )
22 = 6 + ( 84912 / 5307 )
22 = 6 + ( 91248 / 5703 )
22 = 7 + ( 38190 / 2546 )
22 = 7 + ( 39810 / 2654 )
22 = 7 + ( 62085 / 4139 )
22 = 7 + ( 81390 / 5426 )
22 = 7 + ( 81930 / 5462 )
22 = 7 + ( 91245 / 6083 )
22 = 7 + ( 93810 / 6254 )
22 = 7 + ( 98130 / 6542 )
22 = 18 + ( 9504 / 2376 )
————–
23 = 0 + ( 36294 / 1578 )
23 = 0 + ( 81627 / 3549 )
23 = 0 + ( 81972 / 3564 )
23 = 3 + ( 29560 / 1478 )
23 = 3 + ( 91720 / 4586 )
23 = 3 + ( 95620 / 4781 )
23 = 3 + ( 97120 / 4856 )
23 = 5 + ( 71028 / 3946 )
23 = 7 + ( 34960 / 2185 )
23 = 7 + ( 98320 / 6145 )
23 = 8 + ( 40695 / 2713 )
23 = 8 + ( 40965 / 2731 )
23 = 8 + ( 46905 / 3127 )
23 = 8 + ( 49065 / 3271 )
23 = 9 + ( 20538 / 1467 )
23 = 9 + ( 23058 / 1647 )
23 = 9 + ( 23856 / 1704 )
23 = 9 + ( 25704 / 1836 )
23 = 9 + ( 30576 / 2184 )
23 = 9 + ( 51072 / 3648 )
23 = 9 + ( 51408 / 3672 )
23 = 9 + ( 56238 / 4017 )
23 = 9 + ( 57162 / 4083 )
23 = 9 + ( 80136 / 5724 )
23 = 21 + ( 6970 / 3485 )
23 = 21 + ( 7096 / 3548 )
23 = 21 + ( 7690 / 3845 )
23 = 21 + ( 9076 / 4538 )
23 = 21 + ( 9370 / 4685 )
23 = 21 + ( 9670 / 4835 )
23 = 21 + ( 9706 / 4853 )
23 = 21 + ( 9730 / 4865 )
————–
24 = 0 + ( 39528 / 1647 )
24 = 0 + ( 46872 / 1953 )
24 = 2 + ( 43076 / 1958 )
24 = 2 + ( 43670 / 1985 )
24 = 2 + ( 79508 / 3614 )
24 = 5 + ( 70148 / 3692 )
24 = 6 + ( 57402 / 3189 )
24 = 6 + ( 70524 / 3918 )
24 = 6 + ( 81702 / 4539 )
24 = 6 + ( 93204 / 5178 )
24 = 8 + ( 70256 / 4391 )
24 = 9 + ( 23760 / 1584 )
24 = 9 + ( 24570 / 1638 )
24 = 9 + ( 27540 / 1836 )
24 = 9 + ( 38610 / 2574 )
24 = 9 + ( 43065 / 2871 )
24 = 9 + ( 47520 / 3168 )
24 = 9 + ( 54270 / 3618 )
24 = 9 + ( 57240 / 3816 )
24 = 9 + ( 62370 / 4158 )
24 = 9 + ( 86130 / 5742 )
24 = 20 + ( 7436 / 1859 )
————–
25 = 1 + ( 49368 / 2057 )
25 = 1 + ( 78096 / 3254 )
25 = 3 + ( 89562 / 4071 )
25 = 6 + ( 40983 / 2157 )
25 = 6 + ( 57912 / 3048 )
25 = 6 + ( 75012 / 3948 )
25 = 6 + ( 91257 / 4803 )
25 = 7 + ( 34056 / 1892 )
25 = 7 + ( 35028 / 1946 )
25 = 7 + ( 69210 / 3845 )
25 = 7 + ( 93024 / 5168 )
25 = 9 + ( 23760 / 1485 )
————–
26 = 0 + ( 42978 / 1653 )
26 = 0 + ( 56498 / 2173 )
26 = 0 + ( 61854 / 2379 )
26 = 0 + ( 67314 / 2589 )
26 = 0 + ( 67418 / 2593 )
26 = 0 + ( 76518 / 2943 )
26 = 0 + ( 82654 / 3179 )
26 = 0 + ( 89726 / 3451 )
26 = 0 + ( 92846 / 3571 )
26 = 3 + ( 24587 / 1069 )
26 = 6 + ( 34580 / 1729 )
26 = 6 + ( 35840 / 1792 )
26 = 6 + ( 38540 / 1927 )
26 = 6 + ( 43580 / 2179 )
26 = 6 + ( 47180 / 2359 )
26 = 6 + ( 54380 / 2719 )
26 = 6 + ( 58340 / 2917 )
26 = 6 + ( 71840 / 3592 )
26 = 7 + ( 30286 / 1594 )
26 = 8 + ( 57042 / 3169 )
26 = 9 + ( 26078 / 1534 )
26 = 9 + ( 34867 / 2051 )
26 = 9 + ( 35768 / 2104 )
26 = 9 + ( 46801 / 2753 )
26 = 9 + ( 47651 / 2803 )
26 = 9 + ( 51476 / 3028 )
26 = 9 + ( 51782 / 3046 )
26 = 9 + ( 52768 / 3104 )
26 = 9 + ( 54026 / 3178 )
26 = 9 + ( 54706 / 3218 )
26 = 9 + ( 58072 / 3416 )
26 = 9 + ( 68357 / 4021 )
26 = 9 + ( 68527 / 4031 )
26 = 9 + ( 71536 / 4208 )
26 = 9 + ( 78251 / 4603 )
26 = 9 + ( 80512 / 4736 )
26 = 9 + ( 86241 / 5073 )
26 = 9 + ( 86734 / 5102 )
26 = 24 + ( 6158 / 3079 )
————–
27 = 0 + ( 39852 / 1476 )
27 = 0 + ( 49572 / 1836 )
27 = 0 + ( 69741 / 2583 )
27 = 0 + ( 96714 / 3582 )
27 = 2 + ( 36950 / 1478 )
27 = 2 + ( 91850 / 3674 )
27 = 3 + ( 40752 / 1698 )
27 = 3 + ( 57816 / 2409 )
27 = 3 + ( 71640 / 2985 )
27 = 5 + ( 70268 / 3194 )
27 = 5 + ( 76802 / 3491 )
27 = 5 + ( 86702 / 3941 )
27 = 9 + ( 26730 / 1485 )
27 = 9 + ( 57024 / 3168 )
27 = 23 + ( 6980 / 1745 )
————–
28 = 0 + ( 75348 / 2691 )
28 = 1 + ( 56349 / 2087 )
28 = 3 + ( 61950 / 2478 )
28 = 6 + ( 47058 / 2139 )
28 = 9 + ( 72504 / 3816 )
28 = 9 + ( 86013 / 4527 )
————–
29 = 0 + ( 37584 / 1296 )
29 = 0 + ( 73689 / 2541 )
29 = 1 + ( 85792 / 3064 )
29 = 2 + ( 53406 / 1978 )
29 = 2 + ( 94716 / 3508 )
29 = 5 + ( 39048 / 1627 )
29 = 6 + ( 50347 / 2189 )
29 = 6 + ( 54901 / 2387 )
29 = 6 + ( 57109 / 2483 )
29 = 6 + ( 71254 / 3098 )
29 = 6 + ( 85192 / 3704 )
29 = 6 + ( 92851 / 4037 )
29 = 9 + ( 34560 / 1728 )
29 = 9 + ( 35280 / 1764 )
29 = 9 + ( 35640 / 1782 )
29 = 9 + ( 36540 / 1827 )
29 = 9 + ( 43560 / 2178 )
29 = 9 + ( 47160 / 2358 )
29 = 9 + ( 54360 / 2718 )
29 = 9 + ( 56340 / 2817 )
29 = 9 + ( 71280 / 3564 )
29 = 9 + ( 71640 / 3582 )
29 = 9 + ( 83520 / 4176 )
29 = 9 + ( 87120 / 4356 )
29 = 23 + ( 8790 / 1465 )
29 = 23 + ( 9870 / 1645 )
29 = 24 + ( 6790 / 1358 )
29 = 24 + ( 7690 / 1538 )
29 = 24 + ( 7930 / 1586 )
29 = 26 + ( 9174 / 3058 )
29 = 27 + ( 3096 / 1548 )
29 = 27 + ( 3690 / 1845 )
29 = 27 + ( 9036 / 4518 )
29 = 27 + ( 9630 / 4815 )
————–
30 = 3 + ( 70146 / 2598 )
30 = 6 + ( 74592 / 3108 )
30 = 8 + ( 46970 / 2135 )
30 = 23 + ( 7658 / 1094 )
30 = 27 + ( 5049 / 1683 )
30 = 27 + ( 9504 / 3168 )
————–
31 = 3 + ( 71904 / 2568 )
31 = 6 + ( 48075 / 1923 )
31 = 6 + ( 80475 / 3219 )
31 = 6 + ( 92850 / 3714 )
31 = 7 + ( 82056 / 3419 )
31 = 7 + ( 84216 / 3509 )
31 = 9 + ( 32076 / 1458 )
31 = 9 + ( 32670 / 1485 )
31 = 9 + ( 58014 / 2637 )
31 = 9 + ( 78012 / 3546 )
31 = 27 + ( 4356 / 1089 )
————–
32 = 0 + ( 75168 / 2349 )
32 = 3 + ( 47908 / 1652 )
32 = 3 + ( 50692 / 1748 )
32 = 3 + ( 52084 / 1796 )
32 = 7 + ( 96025 / 3841 )
32 = 8 + ( 45672 / 1903 )
32 = 8 + ( 56904 / 2371 )
32 = 8 + ( 72456 / 3019 )
32 = 8 + ( 97512 / 4063 )
32 = 9 + ( 38502 / 1674 )
32 = 9 + ( 43056 / 1872 )
32 = 9 + ( 46851 / 2037 )
32 = 9 + ( 57063 / 2481 )
32 = 9 + ( 82041 / 3567 )
32 = 9 + ( 85146 / 3702 )
32 = 23 + ( 9756 / 1084 )
32 = 25 + ( 7483 / 1069 )
32 = 26 + ( 7854 / 1309 )
32 = 28 + ( 6940 / 1735 )
32 = 29 + ( 5034 / 1678 )
32 = 29 + ( 5304 / 1768 )
32 = 30 + ( 2956 / 1478 )
32 = 30 + ( 9172 / 4586 )
32 = 30 + ( 9562 / 4781 )
32 = 30 + ( 9712 / 4856 )
————–
33 = 8 + ( 40925 / 1637 )
33 = 8 + ( 90425 / 3617 )
33 = 8 + ( 94025 / 3761 )
33 = 9 + ( 35208 / 1467 )
33 = 27 + ( 6534 / 1089 )
————–
34 = 4 + ( 52890 / 1763 )
34 = 4 + ( 95280 / 3176 )
34 = 7 + ( 35046 / 1298 )
34 = 7 + ( 53028 / 1964 )
34 = 9 + ( 42075 / 1683 )
34 = 30 + ( 7824 / 1956 )
————–
35 = 0 + ( 48265 / 1379 )
35 = 0 + ( 63945 / 1827 )
35 = 0 + ( 64295 / 1837 )
35 = 0 + ( 74865 / 2139 )
35 = 0 + ( 93485 / 2671 )
35 = 1 + ( 96730 / 2845 )
35 = 1 + ( 97036 / 2854 )
35 = 2 + ( 54087 / 1639 )
35 = 3 + ( 59072 / 1846 )
35 = 5 + ( 79140 / 2638 )
35 = 6 + ( 49358 / 1702 )
35 = 6 + ( 49532 / 1708 )
35 = 6 + ( 58493 / 2017 )
35 = 7 + ( 54208 / 1936 )
35 = 7 + ( 91504 / 3268 )
35 = 8 + ( 42309 / 1567 )
35 = 9 + ( 36582 / 1407 )
35 = 9 + ( 43082 / 1657 )
35 = 9 + ( 53846 / 2071 )
35 = 9 + ( 54678 / 2103 )
35 = 9 + ( 78546 / 3021 )
35 = 9 + ( 85046 / 3271 )
35 = 30 + ( 6485 / 1297 )
35 = 30 + ( 8645 / 1729 )
————–
36 = 3 + ( 67914 / 2058 )
36 = 6 + ( 53820 / 1794 )
36 = 9 + ( 34506 / 1278 )
36 = 32 + ( 6980 / 1745 )
————–
37 = 0 + ( 65934 / 1782 )
37 = 1 + ( 98460 / 2735 )
37 = 3 + ( 50286 / 1479 )
37 = 3 + ( 97104 / 2856 )
37 = 3 + ( 97410 / 2865 )
37 = 4 + ( 60357 / 1829 )
37 = 7 + ( 54690 / 1823 )
37 = 7 + ( 54960 / 1832 )
37 = 7 + ( 65490 / 2183 )
37 = 7 + ( 69540 / 2318 )
37 = 7 + ( 95460 / 3182 )
37 = 7 + ( 96540 / 3218 )
37 = 9 + ( 71064 / 2538 )
37 = 9 + ( 85176 / 3042 )
————–
38 = 0 + ( 65892 / 1734 )
38 = 0 + ( 74328 / 1956 )
38 = 5 + ( 81609 / 2473 )
38 = 6 + ( 34528 / 1079 )
38 = 6 + ( 83104 / 2597 )
38 = 9 + ( 46023 / 1587 )
38 = 9 + ( 47502 / 1638 )
38 = 9 + ( 50286 / 1734 )
38 = 9 + ( 52374 / 1806 )
38 = 9 + ( 54027 / 1863 )
38 = 25 + ( 10348 / 796 )
38 = 32 + ( 8790 / 1465 )
38 = 32 + ( 9870 / 1645 )
38 = 35 + ( 4827 / 1609 )
38 = 36 + ( 2970 / 1485 )
38 = 36 + ( 4158 / 2079 )
38 = 36 + ( 5418 / 2709 )
38 = 36 + ( 5814 / 2907 )
38 = 36 + ( 9702 / 4851 )
————–
39 = 9 + ( 52380 / 1746 )
39 = 9 + ( 53460 / 1782 )
39 = 9 + ( 65340 / 2178 )
39 = 9 + ( 76140 / 2538 )
39 = 15 + ( 20376 / 849 )
39 = 32 + ( 7658 / 1094 )
39 = 36 + ( 5427 / 1809 )
39 = 36 + ( 5724 / 1908 )
————–
40 = 3 + ( 90687 / 2451 )
40 = 34 + ( 6582 / 1097 )
40 = 37 + ( 5082 / 1694 )
————–
41 = 3 + ( 60724 / 1598 )
41 = 3 + ( 70642 / 1859 )
41 = 4 + ( 76183 / 2059 )
41 = 7 + ( 43690 / 1285 )
41 = 9 + ( 34752 / 1086 )
41 = 9 + ( 65184 / 2037 )
41 = 17 + ( 23640 / 985 )
41 = 23 + ( 10764 / 598 )
41 = 26 + ( 14370 / 958 )
41 = 32 + ( 9756 / 1084 )
41 = 36 + ( 7290 / 1458 )
41 = 36 + ( 7920 / 1584 )
41 = 36 + ( 9270 / 1854 )
41 = 39 + ( 4156 / 2078 )
41 = 39 + ( 5416 / 2708 )
41 = 39 + ( 5614 / 2807 )
41 = 39 + ( 8152 / 4076 )
————–
42 = 2 + ( 74360 / 1859 )
42 = 8 + ( 50762 / 1493 )
42 = 8 + ( 59024 / 1736 )
42 = 8 + ( 69734 / 2051 )
42 = 8 + ( 73406 / 2159 )
42 = 8 + ( 74630 / 2195 )
42 = 15 + ( 23409 / 867 )
42 = 23 + ( 15086 / 794 )
42 = 23 + ( 18506 / 974 )
42 = 38 + ( 5096 / 1274 )
42 = 39 + ( 6174 / 2058 )
————–
43 = 0 + ( 93654 / 2178 )
43 = 1 + ( 86394 / 2057 )
43 = 3 + ( 78240 / 1956 )
43 = 6 + ( 75813 / 2049 )
43 = 7 + ( 90468 / 2513 )
43 = 9 + ( 62730 / 1845 )
43 = 18 + ( 24075 / 963 )
43 = 25 + ( 16074 / 893 )
43 = 27 + ( 15408 / 963 )
43 = 39 + ( 5628 / 1407 )
43 = 40 + ( 5289 / 1763 )
43 = 40 + ( 9528 / 3176 )
————–
44 = 0 + ( 58476 / 1329 )
44 = 0 + ( 59268 / 1347 )
44 = 0 + ( 67892 / 1543 )
44 = 0 + ( 69432 / 1578 )
44 = 0 + ( 95348 / 2167 )
44 = 4 + ( 69520 / 1738 )
44 = 4 + ( 78520 / 1963 )
44 = 6 + ( 79154 / 2083 )
44 = 9 + ( 62405 / 1783 )
44 = 9 + ( 63245 / 1807 )
44 = 9 + ( 76405 / 2183 )
44 = 15 + ( 23084 / 796 )
44 = 15 + ( 27086 / 934 )
44 = 15 + ( 28043 / 967 )
44 = 15 + ( 28304 / 976 )
44 = 24 + ( 13580 / 679 )
44 = 24 + ( 15380 / 769 )
44 = 24 + ( 15860 / 793 )
44 = 25 + ( 16093 / 847 )
44 = 27 + ( 14603 / 859 )
44 = 27 + ( 15368 / 904 )
44 = 27 + ( 15436 / 908 )
44 = 35 + ( 9648 / 1072 )
44 = 36 + ( 8472 / 1059 )
44 = 36 + ( 8592 / 1074 )
44 = 36 + ( 8752 / 1094 )
44 = 38 + ( 9402 / 1567 )
44 = 39 + ( 7280 / 1456 )
44 = 39 + ( 7640 / 1528 )
44 = 39 + ( 7820 / 1564 )
44 = 39 + ( 8270 / 1654 )
44 = 40 + ( 6952 / 1738 )
44 = 40 + ( 7852 / 1963 )
44 = 42 + ( 6158 / 3079 )
————–
45 = 8 + ( 90761 / 2453 )
————–
46 = 0 + ( 58374 / 1269 )
46 = 4 + ( 89670 / 2135 )
46 = 6 + ( 58920 / 1473 )
46 = 7 + ( 91806 / 2354 )
46 = 28 + ( 10674 / 593 )
46 = 34 + ( 10752 / 896 )
46 = 37 + ( 9468 / 1052 )
————–
47 = 4 + ( 56287 / 1309 )
47 = 8 + ( 75036 / 1924 )
47 = 10 + ( 28453 / 769 )
47 = 15 + ( 30784 / 962 )
47 = 23 + ( 10968 / 457 )
47 = 23 + ( 18096 / 754 )
47 = 24 + ( 13087 / 569 )
47 = 24 + ( 13708 / 596 )
47 = 24 + ( 15709 / 683 )
47 = 40 + ( 8659 / 1237 )
47 = 42 + ( 6790 / 1358 )
47 = 42 + ( 7690 / 1538 )
47 = 42 + ( 7930 / 1586 )
47 = 45 + ( 7218 / 3609 )
47 = 45 + ( 7812 / 3906 )
————–
48 = 9 + ( 60372 / 1548 )
48 = 9 + ( 72306 / 1854 )
48 = 23 + ( 17450 / 698 )
48 = 26 + ( 10538 / 479 )
48 = 45 + ( 3267 / 1089 )
48 = 45 + ( 3807 / 1269 )
48 = 45 + ( 8019 / 2673 )
48 = 45 + ( 8073 / 2691 )
48 = 45 + ( 9261 / 3087 )
48 = 45 + ( 9801 / 3267 )
————–
49 = 3 + ( 98670 / 2145 )
49 = 4 + ( 59760 / 1328 )
49 = 6 + ( 59082 / 1374 )
49 = 7 + ( 58926 / 1403 )
49 = 9 + ( 54720 / 1368 )
49 = 9 + ( 74520 / 1863 )
49 = 10 + ( 37284 / 956 )
49 = 12 + ( 35076 / 948 )
49 = 27 + ( 13068 / 594 )
49 = 27 + ( 14058 / 639 )
49 = 30 + ( 14592 / 768 )
49 = 43 + ( 6582 / 1097 )
49 = 45 + ( 7236 / 1809 )
49 = 45 + ( 7632 / 1908 )
49 = 45 + ( 8316 / 2079 )
————–
50 = 3 + ( 49726 / 1058 )
50 = 3 + ( 58609 / 1247 )
50 = 3 + ( 79054 / 1682 )
50 = 5 + ( 73890 / 1642 )
50 = 5 + ( 97380 / 2164 )
50 = 7 + ( 83506 / 1942 )
50 = 8 + ( 63294 / 1507 )
50 = 18 + ( 24096 / 753 )
50 = 18 + ( 30624 / 957 )
50 = 28 + ( 16390 / 745 )
50 = 32 + ( 10764 / 598 )
50 = 45 + ( 6390 / 1278 )
50 = 45 + ( 9360 / 1872 )
————–
51 = 2 + ( 83594 / 1706 )
51 = 3 + ( 84096 / 1752 )
51 = 9 + ( 62370 / 1485 )
51 = 17 + ( 29036 / 854 )
51 = 24 + ( 13689 / 507 )
51 = 32 + ( 15086 / 794 )
51 = 32 + ( 18506 / 974 )
51 = 36 + ( 14580 / 972 )
51 = 47 + ( 8156 / 2039 )
————–
52 = 0 + ( 95472 / 1836 )
52 = 3 + ( 78204 / 1596 )
52 = 7 + ( 68940 / 1532 )
52 = 7 + ( 93645 / 2081 )
52 = 12 + ( 35760 / 894 )
52 = 25 + ( 10746 / 398 )
52 = 34 + ( 10728 / 596 )
52 = 34 + ( 17208 / 956 )
52 = 37 + ( 14520 / 968 )
52 = 45 + ( 7623 / 1089 )
52 = 45 + ( 9702 / 1386 )
52 = 49 + ( 5208 / 1736 )
————–
53 = 0 + ( 65879 / 1243 )
53 = 0 + ( 75896 / 1432 )
53 = 0 + ( 84376 / 1592 )
53 = 0 + ( 92538 / 1746 )
53 = 3 + ( 64850 / 1297 )
53 = 3 + ( 86450 / 1729 )
53 = 5 + ( 49728 / 1036 )
53 = 6 + ( 58703 / 1249 )
53 = 6 + ( 72098 / 1534 )
53 = 6 + ( 72803 / 1549 )
53 = 9 + ( 45628 / 1037 )
53 = 9 + ( 45672 / 1038 )
53 = 9 + ( 47652 / 1083 )
53 = 9 + ( 65032 / 1478 )
53 = 9 + ( 67408 / 1532 )
53 = 9 + ( 72380 / 1645 )
53 = 9 + ( 74052 / 1683 )
53 = 10 + ( 35647 / 829 )
53 = 15 + ( 30248 / 796 )
53 = 18 + ( 23590 / 674 )
53 = 18 + ( 25690 / 734 )
53 = 18 + ( 26390 / 754 )
53 = 23 + ( 19740 / 658 )
53 = 24 + ( 16907 / 583 )
53 = 25 + ( 19684 / 703 )
53 = 27 + ( 15834 / 609 )
53 = 28 + ( 17350 / 694 )
53 = 30 + ( 21758 / 946 )
53 = 34 + ( 10792 / 568 )
53 = 35 + ( 16704 / 928 )
53 = 35 + ( 17028 / 946 )
53 = 36 + ( 14059 / 827 )
53 = 36 + ( 15708 / 924 )
53 = 45 + ( 8296 / 1037 )
53 = 45 + ( 8632 / 1079 )
53 = 45 + ( 8736 / 1092 )
53 = 50 + ( 7914 / 2638 )
————–
54 = 27 + ( 16038 / 594 )
54 = 35 + ( 17024 / 896 )
————–
55 = 3 + ( 56784 / 1092 )
55 = 6 + ( 58947 / 1203 )
55 = 12 + ( 36507 / 849 )
55 = 13 + ( 29568 / 704 )
55 = 15 + ( 37680 / 942 )
55 = 18 + ( 24309 / 657 )
55 = 27 + ( 13860 / 495 )
55 = 36 + ( 15048 / 792 )
55 = 37 + ( 14562 / 809 )
55 = 43 + ( 10752 / 896 )
55 = 48 + ( 7392 / 1056 )
55 = 51 + ( 8376 / 2094 )
————–
56 = 6 + ( 92350 / 1847 )
56 = 10 + ( 29578 / 643 )
56 = 26 + ( 17490 / 583 )
56 = 32 + ( 10968 / 457 )
56 = 32 + ( 18096 / 754 )
56 = 34 + ( 21076 / 958 )
56 = 34 + ( 21670 / 985 )
56 = 36 + ( 14580 / 729 )
56 = 36 + ( 15840 / 792 )
56 = 36 + ( 18540 / 927 )
56 = 53 + ( 4827 / 1609 )
56 = 54 + ( 7218 / 3609 )
56 = 54 + ( 7812 / 3906 )
————–
57 = 2 + ( 74690 / 1358 )
57 = 2 + ( 95480 / 1736 )
57 = 3 + ( 94608 / 1752 )
57 = 3 + ( 97524 / 1806 )
57 = 5 + ( 70928 / 1364 )
57 = 5 + ( 73268 / 1409 )
57 = 9 + ( 76032 / 1584 )
57 = 9 + ( 80352 / 1674 )
57 = 12 + ( 40365 / 897 )
57 = 14 + ( 28079 / 653 )
57 = 17 + ( 23840 / 596 )
57 = 17 + ( 38240 / 956 )
57 = 18 + ( 37206 / 954 )
57 = 30 + ( 21546 / 798 )
57 = 32 + ( 17450 / 698 )
57 = 39 + ( 10476 / 582 )
57 = 39 + ( 14526 / 807 )
57 = 50 + ( 9674 / 1382 )
57 = 54 + ( 3267 / 1089 )
57 = 54 + ( 3807 / 1269 )
57 = 54 + ( 8019 / 2673 )
57 = 54 + ( 8073 / 2691 )
57 = 54 + ( 9261 / 3087 )
57 = 54 + ( 9801 / 3267 )
————–
58 = 3 + ( 68970 / 1254 )
58 = 3 + ( 79860 / 1452 )
58 = 10 + ( 23856 / 497 )
58 = 15 + ( 20769 / 483 )
58 = 18 + ( 23760 / 594 )
58 = 21 + ( 35076 / 948 )
58 = 36 + ( 12078 / 549 )
58 = 39 + ( 15276 / 804 )
58 = 54 + ( 7236 / 1809 )
58 = 54 + ( 7632 / 1908 )
58 = 54 + ( 8316 / 2079 )
————–
59 = 0 + ( 73986 / 1254 )
59 = 2 + ( 59736 / 1048 )
59 = 7 + ( 80392 / 1546 )
59 = 7 + ( 96304 / 1852 )
59 = 9 + ( 64350 / 1287 )
59 = 9 + ( 82350 / 1647 )
59 = 12 + ( 35908 / 764 )
59 = 14 + ( 35820 / 796 )
59 = 17 + ( 40236 / 958 )
59 = 19 + ( 25480 / 637 )
59 = 30 + ( 17284 / 596 )
59 = 30 + ( 24679 / 851 )
59 = 39 + ( 14560 / 728 )
59 = 39 + ( 15280 / 764 )
59 = 39 + ( 15640 / 782 )
59 = 39 + ( 16540 / 827 )
59 = 45 + ( 10962 / 783 )
59 = 45 + ( 12306 / 879 )
59 = 45 + ( 13608 / 972 )
59 = 52 + ( 7483 / 1069 )
59 = 54 + ( 6390 / 1278 )
59 = 54 + ( 9360 / 1872 )
59 = 57 + ( 4138 / 2069 )
59 = 57 + ( 4186 / 2093 )
59 = 57 + ( 4618 / 2309 )
59 = 57 + ( 6184 / 3092 )
59 = 57 + ( 6418 / 3209 )
————–
60 = 3 + ( 89604 / 1572 )
60 = 8 + ( 67340 / 1295 )
60 = 8 + ( 72956 / 1403 )
60 = 12 + ( 43056 / 897 )
60 = 15 + ( 39420 / 876 )
————–
61 = 3 + ( 92046 / 1587 )
61 = 18 + ( 23607 / 549 )
61 = 18 + ( 34056 / 792 )
61 = 21 + ( 35760 / 894 )
61 = 27 + ( 16830 / 495 )
61 = 28 + ( 15609 / 473 )
61 = 36 + ( 20475 / 819 )
61 = 37 + ( 14592 / 608 )
61 = 37 + ( 21504 / 896 )
61 = 43 + ( 10728 / 596 )
61 = 43 + ( 17208 / 956 )
61 = 54 + ( 7623 / 1089 )
61 = 54 + ( 9702 / 1386 )
61 = 57 + ( 4368 / 1092 )
61 = 57 + ( 4836 / 1209 )
61 = 57 + ( 8364 / 2091 )
61 = 57 + ( 8436 / 2109 )
————–
62 = 0 + ( 79546 / 1283 )
62 = 0 + ( 94736 / 1528 )
62 = 6 + ( 83720 / 1495 )
62 = 6 + ( 84392 / 1507 )
62 = 9 + ( 54378 / 1026 )
62 = 9 + ( 57346 / 1082 )
62 = 9 + ( 72504 / 1368 )
62 = 12 + ( 34850 / 697 )
62 = 12 + ( 38450 / 769 )
62 = 12 + ( 46850 / 937 )
62 = 12 + ( 48350 / 967 )
62 = 12 + ( 48650 / 973 )
62 = 15 + ( 37694 / 802 )
62 = 18 + ( 27940 / 635 )
62 = 18 + ( 35024 / 796 )
62 = 24 + ( 15086 / 397 )
62 = 27 + ( 16905 / 483 )
62 = 27 + ( 18690 / 534 )
62 = 27 + ( 30415 / 869 )
62 = 27 + ( 34510 / 986 )
62 = 30 + ( 15296 / 478 )
62 = 30 + ( 15872 / 496 )
62 = 30 + ( 17984 / 562 )
62 = 32 + ( 19740 / 658 )
62 = 35 + ( 12906 / 478 )
62 = 35 + ( 20196 / 748 )
62 = 36 + ( 12870 / 495 )
62 = 36 + ( 20514 / 789 )
62 = 36 + ( 21970 / 845 )
62 = 39 + ( 10856 / 472 )
62 = 40 + ( 16258 / 739 )
62 = 42 + ( 13580 / 679 )
62 = 42 + ( 15380 / 769 )
62 = 42 + ( 15860 / 793 )
62 = 43 + ( 10792 / 568 )
62 = 45 + ( 10829 / 637 )
62 = 53 + ( 9648 / 1072 )
62 = 54 + ( 8296 / 1037 )
62 = 54 + ( 8632 / 1079 )
62 = 54 + ( 8736 / 1092 )
62 = 57 + ( 6920 / 1384 )
62 = 57 + ( 9230 / 1846 )
62 = 57 + ( 9320 / 1864 )
62 = 59 + ( 7104 / 2368 )
62 = 60 + ( 3458 / 1729 )
62 = 60 + ( 3584 / 1792 )
62 = 60 + ( 3854 / 1927 )
62 = 60 + ( 4358 / 2179 )
62 = 60 + ( 4718 / 2359 )
62 = 60 + ( 5438 / 2719 )
62 = 60 + ( 5834 / 2917 )
62 = 60 + ( 7184 / 3592 )
————–
63 = 9 + ( 57348 / 1062 )
63 = 18 + ( 26730 / 594 )
63 = 18 + ( 35640 / 792 )
63 = 35 + ( 27104 / 968 )
63 = 36 + ( 18954 / 702 )
63 = 36 + ( 24057 / 891 )
63 = 39 + ( 15048 / 627 )
63 = 59 + ( 7304 / 1826 )
63 = 60 + ( 5382 / 1794 )
————–
64 = 7 + ( 62358 / 1094 )
64 = 7 + ( 89034 / 1562 )
64 = 9 + ( 75240 / 1368 )
64 = 15 + ( 34692 / 708 )
64 = 21 + ( 36507 / 849 )
64 = 24 + ( 31560 / 789 )
64 = 24 + ( 35160 / 879 )
64 = 36 + ( 25704 / 918 )
64 = 37 + ( 24516 / 908 )
64 = 57 + ( 8463 / 1209 )
64 = 60 + ( 5892 / 1473 )
————–
65 = 6 + ( 90742 / 1538 )
65 = 8 + ( 95304 / 1672 )
65 = 9 + ( 58632 / 1047 )
65 = 13 + ( 50284 / 967 )
65 = 25 + ( 31840 / 796 )
65 = 26 + ( 30459 / 781 )
65 = 27 + ( 15048 / 396 )
65 = 35 + ( 27480 / 916 )
65 = 42 + ( 13087 / 569 )
65 = 42 + ( 13708 / 596 )
65 = 42 + ( 15709 / 683 )
65 = 43 + ( 21076 / 958 )
65 = 43 + ( 21670 / 985 )
65 = 45 + ( 12780 / 639 )
65 = 45 + ( 18720 / 936 )
65 = 52 + ( 10348 / 796 )
65 = 56 + ( 9378 / 1042 )
65 = 58 + ( 9604 / 1372 )
65 = 60 + ( 9235 / 1847 )
65 = 62 + ( 9174 / 3058 )
65 = 63 + ( 2970 / 1485 )
65 = 63 + ( 4158 / 2079 )
65 = 63 + ( 5418 / 2709 )
65 = 63 + ( 5814 / 2907 )
65 = 63 + ( 9702 / 4851 )
————–
66 = 0 + ( 83754 / 1269 )
66 = 18 + ( 23760 / 495 )
66 = 21 + ( 40365 / 897 )
66 = 36 + ( 17820 / 594 )
66 = 36 + ( 24570 / 819 )
66 = 36 + ( 27540 / 918 )
66 = 50 + ( 14768 / 923 )
66 = 63 + ( 5427 / 1809 )
66 = 63 + ( 5724 / 1908 )
————–
67 = 3 + ( 79680 / 1245 )
67 = 10 + ( 32946 / 578 )
67 = 13 + ( 27486 / 509 )
67 = 18 + ( 29547 / 603 )
67 = 27 + ( 15840 / 396 )
67 = 27 + ( 18360 / 459 )
67 = 27 + ( 35640 / 891 )
67 = 27 + ( 38160 / 954 )
67 = 28 + ( 19734 / 506 )
67 = 30 + ( 25419 / 687 )
67 = 39 + ( 21504 / 768 )
67 = 45 + ( 16038 / 729 )
67 = 45 + ( 19206 / 873 )
————–
68 = 0 + ( 98736 / 1452 )
68 = 2 + ( 68574 / 1039 )
68 = 3 + ( 95680 / 1472 )
68 = 5 + ( 82467 / 1309 )
68 = 12 + ( 43960 / 785 )
68 = 16 + ( 30784 / 592 )
68 = 16 + ( 39208 / 754 )
68 = 18 + ( 36450 / 729 )
68 = 18 + ( 46350 / 927 )
68 = 19 + ( 26803 / 547 )
68 = 21 + ( 35908 / 764 )
68 = 26 + ( 41370 / 985 )
68 = 28 + ( 15760 / 394 )
68 = 28 + ( 17560 / 439 )
68 = 29 + ( 18057 / 463 )
68 = 30 + ( 21964 / 578 )
68 = 30 + ( 25498 / 671 )
68 = 39 + ( 17458 / 602 )
68 = 45 + ( 20631 / 897 )
68 = 49 + ( 16207 / 853 )
68 = 50 + ( 13842 / 769 )
68 = 50 + ( 14328 / 796 )
68 = 50 + ( 14976 / 832 )
68 = 54 + ( 10962 / 783 )
68 = 54 + ( 12306 / 879 )
68 = 54 + ( 13608 / 972 )
68 = 62 + ( 7854 / 1309 )
68 = 63 + ( 7290 / 1458 )
68 = 63 + ( 7920 / 1584 )
68 = 63 + ( 9270 / 1854 )
————–
69 = 14 + ( 32780 / 596 )
69 = 15 + ( 48762 / 903 )
69 = 17 + ( 48620 / 935 )
69 = 21 + ( 43056 / 897 )
69 = 24 + ( 30915 / 687 )
69 = 24 + ( 39015 / 867 )
69 = 39 + ( 17460 / 582 )
69 = 42 + ( 13689 / 507 )
————–
70 = 16 + ( 40932 / 758 )
70 = 16 + ( 42390 / 785 )
70 = 37 + ( 15906 / 482 )
70 = 48 + ( 15906 / 723 )
70 = 52 + ( 16074 / 893 )
70 = 67 + ( 5802 / 1934 )
————–
71 = 3 + ( 74528 / 1096 )
71 = 6 + ( 80795 / 1243 )
71 = 6 + ( 84305 / 1297 )
71 = 9 + ( 74586 / 1203 )
71 = 9 + ( 76508 / 1234 )
71 = 9 + ( 78430 / 1265 )
71 = 9 + ( 84072 / 1356 )
71 = 9 + ( 85064 / 1372 )
71 = 13 + ( 50692 / 874 )
71 = 15 + ( 27608 / 493 )
71 = 15 + ( 38024 / 679 )
71 = 16 + ( 20845 / 379 )
71 = 18 + ( 25069 / 473 )
71 = 19 + ( 30472 / 586 )
71 = 21 + ( 34850 / 697 )
71 = 21 + ( 38450 / 769 )
71 = 21 + ( 46850 / 937 )
71 = 21 + ( 48350 / 967 )
71 = 21 + ( 48650 / 973 )
71 = 27 + ( 16940 / 385 )
71 = 27 + ( 35904 / 816 )
71 = 36 + ( 18970 / 542 )
71 = 36 + ( 24815 / 709 )
71 = 37 + ( 29104 / 856 )
71 = 37 + ( 29410 / 865 )
71 = 42 + ( 16907 / 583 )
71 = 45 + ( 20618 / 793 )
71 = 52 + ( 16093 / 847 )
71 = 53 + ( 16704 / 928 )
71 = 53 + ( 17028 / 946 )
71 = 54 + ( 10829 / 637 )
71 = 56 + ( 14730 / 982 )
71 = 63 + ( 8472 / 1059 )
71 = 63 + ( 8592 / 1074 )
71 = 63 + ( 8752 / 1094 )
71 = 69 + ( 2708 / 1354 )
71 = 69 + ( 2870 / 1435 )
71 = 69 + ( 3704 / 1852 )
71 = 69 + ( 4370 / 2185 )
71 = 69 + ( 7028 / 3514 )
71 = 69 + ( 7082 / 3541 )
71 = 69 + ( 8270 / 4135 )
71 = 69 + ( 8702 / 4351 )
————–
72 = 5 + ( 69278 / 1034 )
72 = 14 + ( 53708 / 926 )
72 = 17 + ( 29480 / 536 )
72 = 17 + ( 53240 / 968 )
72 = 17 + ( 54230 / 986 )
72 = 18 + ( 26730 / 495 )
72 = 18 + ( 32076 / 594 )
72 = 20 + ( 39416 / 758 )
72 = 24 + ( 38160 / 795 )
72 = 26 + ( 37490 / 815 )
72 = 36 + ( 17820 / 495 )
72 = 53 + ( 17024 / 896 )
72 = 57 + ( 13860 / 924 )
————–
73 = 6 + ( 92058 / 1374 )
73 = 7 + ( 83490 / 1265 )
73 = 10 + ( 36792 / 584 )
73 = 10 + ( 54936 / 872 )
73 = 13 + ( 56820 / 947 )
73 = 18 + ( 32670 / 594 )
73 = 18 + ( 43560 / 792 )
73 = 18 + ( 53460 / 972 )
73 = 30 + ( 29154 / 678 )
73 = 30 + ( 29541 / 687 )
73 = 31 + ( 29568 / 704 )
73 = 39 + ( 15708 / 462 )
73 = 70 + ( 5469 / 1823 )
73 = 70 + ( 5496 / 1832 )
73 = 70 + ( 6549 / 2183 )
73 = 70 + ( 6954 / 2318 )
73 = 70 + ( 9546 / 3182 )
73 = 70 + ( 9654 / 3218 )
————–
74 = 2 + ( 97056 / 1348 )
74 = 4 + ( 86590 / 1237 )
74 = 5 + ( 96738 / 1402 )
74 = 15 + ( 40297 / 683 )
74 = 19 + ( 45760 / 832 )
74 = 45 + ( 10962 / 378 )
74 = 45 + ( 26013 / 897 )
74 = 45 + ( 26187 / 903 )
74 = 54 + ( 12780 / 639 )
74 = 54 + ( 18720 / 936 )
74 = 58 + ( 12304 / 769 )
74 = 60 + ( 13258 / 947 )
74 = 65 + ( 9378 / 1042 )
74 = 72 + ( 3096 / 1548 )
74 = 72 + ( 3690 / 1845 )
74 = 72 + ( 9036 / 4518 )
74 = 72 + ( 9630 / 4815 )
————–
75 = 3 + ( 76248 / 1059 )
75 = 5 + ( 96740 / 1382 )
75 = 6 + ( 75348 / 1092 )
75 = 17 + ( 29348 / 506 )
75 = 18 + ( 43092 / 756 )
75 = 45 + ( 26190 / 873 )
75 = 45 + ( 26730 / 891 )
75 = 47 + ( 26180 / 935 )
75 = 51 + ( 20376 / 849 )
75 = 60 + ( 12735 / 849 )
75 = 72 + ( 5049 / 1683 )
75 = 72 + ( 9504 / 3168 )
————–
76 = 10 + ( 25674 / 389 )
76 = 19 + ( 43206 / 758 )
76 = 28 + ( 19536 / 407 )
76 = 39 + ( 24087 / 651 )
76 = 46 + ( 25170 / 839 )
76 = 54 + ( 16038 / 729 )
76 = 54 + ( 19206 / 873 )
76 = 60 + ( 14352 / 897 )
76 = 72 + ( 4356 / 1089 )
76 = 73 + ( 5082 / 1694 )
————–
77 = 5 + ( 89064 / 1237 )
77 = 10 + ( 24589 / 367 )
77 = 10 + ( 62578 / 934 )
77 = 10 + ( 63784 / 952 )
77 = 12 + ( 37960 / 584 )
77 = 12 + ( 38740 / 596 )
77 = 12 + ( 45370 / 698 )
77 = 18 + ( 29736 / 504 )
77 = 19 + ( 20764 / 358 )
77 = 21 + ( 43960 / 785 )
77 = 25 + ( 19084 / 367 )
77 = 27 + ( 18450 / 369 )
77 = 27 + ( 48150 / 963 )
77 = 29 + ( 36048 / 751 )
77 = 39 + ( 10564 / 278 )
77 = 45 + ( 12096 / 378 )
77 = 49 + ( 10528 / 376 )
77 = 54 + ( 20631 / 897 )
77 = 57 + ( 13840 / 692 )
77 = 57 + ( 18460 / 923 )
77 = 57 + ( 18640 / 932 )
77 = 62 + ( 14370 / 958 )
77 = 75 + ( 4138 / 2069 )
77 = 75 + ( 4186 / 2093 )
77 = 75 + ( 4618 / 2309 )
77 = 75 + ( 6184 / 3092 )
77 = 75 + ( 6418 / 3209 )
————–
78 = 18 + ( 39420 / 657 )
78 = 23 + ( 41690 / 758 )
78 = 29 + ( 35084 / 716 )
78 = 39 + ( 15678 / 402 )
78 = 45 + ( 21087 / 639 )
78 = 51 + ( 23409 / 867 )
78 = 63 + ( 14580 / 972 )
78 = 72 + ( 6534 / 1089 )
78 = 74 + ( 8156 / 2039 )
————–
79 = 10 + ( 39468 / 572 )
79 = 16 + ( 24507 / 389 )
79 = 16 + ( 25074 / 398 )
79 = 30 + ( 27489 / 561 )
79 = 39 + ( 28560 / 714 )
79 = 40 + ( 37518 / 962 )
79 = 46 + ( 10857 / 329 )
79 = 52 + ( 10746 / 398 )
79 = 75 + ( 4368 / 1092 )
79 = 75 + ( 4836 / 1209 )
79 = 75 + ( 8364 / 2091 )
79 = 75 + ( 8436 / 2109 )
79 = 76 + ( 5802 / 1934 )
————–
80 = 8 + ( 74592 / 1036 )
80 = 16 + ( 25408 / 397 )
80 = 16 + ( 30592 / 478 )
80 = 18 + ( 26970 / 435 )
80 = 18 + ( 30752 / 496 )
80 = 18 + ( 36704 / 592 )
80 = 18 + ( 56234 / 907 )
80 = 25 + ( 38170 / 694 )
80 = 27 + ( 19504 / 368 )
80 = 27 + ( 50138 / 946 )
80 = 27 + ( 51304 / 968 )
80 = 28 + ( 15964 / 307 )
80 = 35 + ( 41760 / 928 )
80 = 36 + ( 17952 / 408 )
80 = 36 + ( 21780 / 495 )
80 = 36 + ( 42108 / 957 )
80 = 42 + ( 15086 / 397 )
80 = 48 + ( 30752 / 961 )
80 = 51 + ( 23084 / 796 )
80 = 51 + ( 27086 / 934 )
80 = 51 + ( 28043 / 967 )
80 = 51 + ( 28304 / 976 )
80 = 52 + ( 19684 / 703 )
80 = 53 + ( 12906 / 478 )
80 = 53 + ( 20196 / 748 )
80 = 54 + ( 20618 / 793 )
80 = 57 + ( 13892 / 604 )
80 = 58 + ( 20614 / 937 )
80 = 58 + ( 21406 / 973 )
80 = 63 + ( 14059 / 827 )
80 = 63 + ( 15708 / 924 )
80 = 65 + ( 14730 / 982 )
80 = 75 + ( 6920 / 1384 )
80 = 75 + ( 9230 / 1846 )
80 = 75 + ( 9320 / 1864 )
80 = 78 + ( 2690 / 1345 )
80 = 78 + ( 2906 / 1453 )
80 = 78 + ( 2930 / 1465 )
80 = 78 + ( 3092 / 1546 )
80 = 78 + ( 3290 / 1645 )
80 = 78 + ( 6290 / 3145 )
80 = 78 + ( 6902 / 3451 )
80 = 78 + ( 9026 / 4513 )
80 = 78 + ( 9032 / 4516 )
80 = 78 + ( 9062 / 4531 )
80 = 78 + ( 9230 / 4615 )
80 = 78 + ( 9302 / 4651 )
————–
81 = 3 + ( 98046 / 1257 )
81 = 5 + ( 79268 / 1043 )
81 = 18 + ( 40257 / 639 )
81 = 26 + ( 19085 / 347 )
81 = 29 + ( 41756 / 803 )
81 = 45 + ( 32076 / 891 )
81 = 47 + ( 32810 / 965 )
81 = 53 + ( 27104 / 968 )
81 = 78 + ( 9162 / 3054 )
————–
82 = 10 + ( 32976 / 458 )
82 = 27 + ( 51480 / 936 )
82 = 39 + ( 10578 / 246 )
82 = 42 + ( 31560 / 789 )
82 = 42 + ( 35160 / 879 )
82 = 45 + ( 29637 / 801 )
82 = 49 + ( 10758 / 326 )
82 = 63 + ( 15048 / 792 )
82 = 73 + ( 9468 / 1052 )
82 = 75 + ( 8463 / 1209 )
82 = 78 + ( 4236 / 1059 )
————–
83 = 14 + ( 62583 / 907 )
83 = 15 + ( 27064 / 398 )
83 = 15 + ( 60724 / 893 )
83 = 17 + ( 26598 / 403 )
83 = 18 + ( 25740 / 396 )
83 = 18 + ( 49530 / 762 )
83 = 24 + ( 50917 / 863 )
83 = 31 + ( 50284 / 967 )
83 = 50 + ( 23694 / 718 )
83 = 51 + ( 30784 / 962 )
83 = 53 + ( 27480 / 916 )
83 = 54 + ( 10962 / 378 )
83 = 54 + ( 26013 / 897 )
83 = 54 + ( 26187 / 903 )
83 = 60 + ( 13294 / 578 )
83 = 60 + ( 21574 / 938 )
83 = 63 + ( 14580 / 729 )
83 = 63 + ( 15840 / 792 )
83 = 63 + ( 18540 / 927 )
83 = 67 + ( 14320 / 895 )
83 = 79 + ( 5632 / 1408 )
83 = 81 + ( 7092 / 3546 )
83 = 81 + ( 7290 / 3645 )
83 = 81 + ( 9072 / 4536 )
83 = 81 + ( 9270 / 4635 )
————–
84 = 5 + ( 84293 / 1067 )
84 = 14 + ( 36890 / 527 )
84 = 18 + ( 32670 / 495 )
84 = 18 + ( 62370 / 945 )
84 = 26 + ( 57014 / 983 )
84 = 30 + ( 15876 / 294 )
84 = 41 + ( 28079 / 653 )
84 = 54 + ( 26190 / 873 )
84 = 54 + ( 26730 / 891 )
84 = 60 + ( 14328 / 597 )
84 = 62 + ( 10538 / 479 )
84 = 69 + ( 10845 / 723 )
————–
85 = 15 + ( 43890 / 627 )
85 = 18 + ( 53064 / 792 )
85 = 31 + ( 27486 / 509 )
85 = 45 + ( 31680 / 792 )
85 = 45 + ( 32760 / 819 )
85 = 45 + ( 36720 / 918 )
85 = 46 + ( 28509 / 731 )
85 = 46 + ( 35178 / 902 )
85 = 63 + ( 12078 / 549 )
85 = 69 + ( 12048 / 753 )
85 = 70 + ( 12945 / 863 )
85 = 79 + ( 6258 / 1043 )
85 = 81 + ( 9504 / 2376 )
————–
86 = 16 + ( 27580 / 394 )
86 = 16 + ( 38290 / 547 )
86 = 21 + ( 37960 / 584 )
86 = 21 + ( 38740 / 596 )
86 = 21 + ( 45370 / 698 )
86 = 23 + ( 50148 / 796 )
86 = 26 + ( 54780 / 913 )
86 = 27 + ( 38409 / 651 )
86 = 30 + ( 45976 / 821 )
86 = 36 + ( 14850 / 297 )
86 = 40 + ( 35926 / 781 )
86 = 41 + ( 35820 / 796 )
86 = 50 + ( 34812 / 967 )
86 = 54 + ( 12096 / 378 )
86 = 57 + ( 10498 / 362 )
86 = 57 + ( 23461 / 809 )
86 = 82 + ( 6940 / 1735 )
————–
87 = 15 + ( 29376 / 408 )
87 = 23 + ( 50816 / 794 )
87 = 27 + ( 41580 / 693 )
87 = 27 + ( 53460 / 891 )
87 = 30 + ( 16758 / 294 )
87 = 32 + ( 41690 / 758 )
87 = 35 + ( 47216 / 908 )
87 = 42 + ( 30915 / 687 )
87 = 42 + ( 39015 / 867 )
87 = 45 + ( 30618 / 729 )
87 = 47 + ( 15680 / 392 )
87 = 48 + ( 23751 / 609 )
87 = 50 + ( 14726 / 398 )
87 = 54 + ( 21087 / 639 )
87 = 59 + ( 20468 / 731 )
87 = 83 + ( 5096 / 1274 )
————–
88 = 3 + ( 87465 / 1029 )
88 = 10 + ( 37596 / 482 )
88 = 10 + ( 53742 / 689 )
88 = 19 + ( 25806 / 374 )
88 = 36 + ( 14508 / 279 )
88 = 45 + ( 17028 / 396 )
88 = 46 + ( 21378 / 509 )
88 = 48 + ( 23160 / 579 )
88 = 63 + ( 20475 / 819 )
88 = 69 + ( 13452 / 708 )
88 = 72 + ( 15408 / 963 )
88 = 73 + ( 14520 / 968 )
————–
89 = 7 + ( 84952 / 1036 )
89 = 14 + ( 73650 / 982 )
89 = 15 + ( 28046 / 379 )
89 = 15 + ( 49802 / 673 )
89 = 17 + ( 49320 / 685 )
89 = 19 + ( 52360 / 748 )
89 = 25 + ( 19648 / 307 )
89 = 27 + ( 31496 / 508 )
89 = 31 + ( 50692 / 874 )
89 = 37 + ( 46852 / 901 )
89 = 37 + ( 50128 / 964 )
89 = 37 + ( 51064 / 982 )
89 = 45 + ( 13068 / 297 )
89 = 45 + ( 30712 / 698 )
89 = 46 + ( 10879 / 253 )
89 = 51 + ( 30248 / 796 )
89 = 57 + ( 10496 / 328 )
89 = 57 + ( 12608 / 394 )
89 = 57 + ( 12896 / 403 )
89 = 57 + ( 19328 / 604 )
89 = 60 + ( 17342 / 598 )
89 = 63 + ( 12870 / 495 )
89 = 63 + ( 20514 / 789 )
89 = 63 + ( 21970 / 845 )
89 = 72 + ( 14603 / 859 )
89 = 72 + ( 15368 / 904 )
89 = 72 + ( 15436 / 908 )
89 = 83 + ( 9402 / 1567 )
89 = 87 + ( 2690 / 1345 )
89 = 87 + ( 2906 / 1453 )
89 = 87 + ( 2930 / 1465 )
89 = 87 + ( 3092 / 1546 )
89 = 87 + ( 3290 / 1645 )
89 = 87 + ( 6290 / 3145 )
89 = 87 + ( 6902 / 3451 )
89 = 87 + ( 9026 / 4513 )
89 = 87 + ( 9032 / 4516 )
89 = 87 + ( 9062 / 4531 )
89 = 87 + ( 9230 / 4615 )
89 = 87 + ( 9302 / 4651 )
————–
90 = 42 + ( 38160 / 795 )
90 = 45 + ( 17820 / 396 )
90 = 54 + ( 32076 / 891 )
90 = 57 + ( 20394 / 618 )
90 = 57 + ( 31086 / 942 )
90 = 63 + ( 18954 / 702 )
90 = 63 + ( 24057 / 891 )
90 = 75 + ( 13860 / 924 )
90 = 87 + ( 9162 / 3054 )
————–
91 = 18 + ( 36792 / 504 )
91 = 19 + ( 56304 / 782 )
91 = 27 + ( 19584 / 306 )
91 = 27 + ( 31680 / 495 )
91 = 27 + ( 38016 / 594 )
91 = 31 + ( 56820 / 947 )
91 = 34 + ( 51072 / 896 )
91 = 37 + ( 26190 / 485 )
91 = 46 + ( 35190 / 782 )
91 = 51 + ( 37680 / 942 )
91 = 54 + ( 29637 / 801 )
91 = 63 + ( 25704 / 918 )
91 = 73 + ( 14562 / 809 )
91 = 84 + ( 7392 / 1056 )
91 = 87 + ( 4236 / 1059 )
————–
92 = 10 + ( 59368 / 724 )
92 = 18 + ( 37296 / 504 )
92 = 20 + ( 41976 / 583 )
92 = 27 + ( 31590 / 486 )
92 = 27 + ( 38610 / 594 )
92 = 35 + ( 40926 / 718 )
92 = 36 + ( 45192 / 807 )
92 = 46 + ( 32890 / 715 )
92 = 50 + ( 38472 / 916 )
92 = 52 + ( 31840 / 796 )
92 = 59 + ( 12408 / 376 )
92 = 60 + ( 15328 / 479 )
92 = 60 + ( 17248 / 539 )
92 = 62 + ( 17490 / 583 )
92 = 76 + ( 14320 / 895 )
92 = 85 + ( 9604 / 1372 )
92 = 90 + ( 3456 / 1728 )
92 = 90 + ( 3528 / 1764 )
92 = 90 + ( 3564 / 1782 )
92 = 90 + ( 3654 / 1827 )
92 = 90 + ( 4356 / 2178 )
92 = 90 + ( 4716 / 2358 )
92 = 90 + ( 5436 / 2718 )
92 = 90 + ( 5634 / 2817 )
92 = 90 + ( 7128 / 3564 )
92 = 90 + ( 7164 / 3582 )
92 = 90 + ( 8352 / 4176 )
92 = 90 + ( 8712 / 4356 )
————–
93 = 23 + ( 65870 / 941 )
93 = 24 + ( 38709 / 561 )
93 = 24 + ( 56097 / 813 )
93 = 26 + ( 50183 / 749 )
93 = 30 + ( 15687 / 249 )
93 = 35 + ( 47096 / 812 )
93 = 45 + ( 38016 / 792 )
93 = 59 + ( 16082 / 473 )
93 = 63 + ( 17820 / 594 )
93 = 63 + ( 24570 / 819 )
93 = 63 + ( 27540 / 918 )
93 = 68 + ( 10925 / 437 )
93 = 69 + ( 10872 / 453 )
93 = 90 + ( 5238 / 1746 )
93 = 90 + ( 5346 / 1782 )
93 = 90 + ( 6534 / 2178 )
93 = 90 + ( 7614 / 2538 )
————–
94 = 10 + ( 37968 / 452 )
94 = 15 + ( 63042 / 798 )
94 = 18 + ( 37620 / 495 )
94 = 18 + ( 43092 / 567 )
94 = 24 + ( 61530 / 879 )
94 = 25 + ( 48369 / 701 )
94 = 30 + ( 49152 / 768 )
94 = 30 + ( 57216 / 894 )
94 = 30 + ( 61248 / 957 )
94 = 34 + ( 58260 / 971 )
94 = 36 + ( 28710 / 495 )
94 = 36 + ( 47502 / 819 )
94 = 51 + ( 20769 / 483 )
94 = 54 + ( 31680 / 792 )
94 = 54 + ( 32760 / 819 )
94 = 54 + ( 36720 / 918 )
94 = 60 + ( 19482 / 573 )
94 = 64 + ( 25170 / 839 )
94 = 67 + ( 10584 / 392 )
94 = 69 + ( 12075 / 483 )
94 = 69 + ( 21075 / 843 )
94 = 72 + ( 13068 / 594 )
94 = 72 + ( 14058 / 639 )
94 = 79 + ( 10245 / 683 )
94 = 79 + ( 12540 / 836 )
94 = 90 + ( 5472 / 1368 )
94 = 90 + ( 7452 / 1863 )
————–
95 = 3 + ( 94576 / 1028 )
95 = 3 + ( 96784 / 1052 )
95 = 12 + ( 39508 / 476 )
95 = 12 + ( 75364 / 908 )
95 = 13 + ( 78064 / 952 )
95 = 17 + ( 39624 / 508 )
95 = 20 + ( 68475 / 913 )
95 = 23 + ( 50184 / 697 )
95 = 25 + ( 48370 / 691 )
95 = 28 + ( 30619 / 457 )
95 = 28 + ( 45091 / 673 )
95 = 30 + ( 17485 / 269 )
95 = 32 + ( 50148 / 796 )
95 = 35 + ( 41820 / 697 )
95 = 36 + ( 27081 / 459 )
95 = 36 + ( 47259 / 801 )
95 = 39 + ( 27160 / 485 )
95 = 58 + ( 24901 / 673 )
95 = 59 + ( 30276 / 841 )
95 = 71 + ( 23640 / 985 )
95 = 75 + ( 13840 / 692 )
95 = 75 + ( 18460 / 923 )
95 = 75 + ( 18640 / 932 )
95 = 89 + ( 6342 / 1057 )
95 = 90 + ( 6435 / 1287 )
95 = 90 + ( 8235 / 1647 )
95 = 92 + ( 5034 / 1678 )
95 = 92 + ( 5304 / 1768 )
95 = 93 + ( 4156 / 2078 )
95 = 93 + ( 5416 / 2708 )
95 = 93 + ( 5614 / 2807 )
95 = 93 + ( 8152 / 4076 )
————–
96 = 23 + ( 48107 / 659 )
96 = 29 + ( 34706 / 518 )
96 = 30 + ( 65142 / 987 )
96 = 32 + ( 50816 / 794 )
96 = 38 + ( 14906 / 257 )
96 = 39 + ( 14706 / 258 )
96 = 41 + ( 32780 / 596 )
96 = 51 + ( 39420 / 876 )
96 = 54 + ( 30618 / 729 )
96 = 56 + ( 18920 / 473 )
96 = 78 + ( 16254 / 903 )
96 = 89 + ( 7364 / 1052 )
96 = 93 + ( 6174 / 2058 )
————–
97 = 4 + ( 97836 / 1052 )
97 = 19 + ( 28470 / 365 )
97 = 27 + ( 48510 / 693 )
97 = 37 + ( 52140 / 869 )
97 = 40 + ( 16359 / 287 )
97 = 54 + ( 17028 / 396 )
97 = 57 + ( 36480 / 912 )
97 = 57 + ( 36840 / 921 )
97 = 60 + ( 15873 / 429 )
97 = 64 + ( 10857 / 329 )
97 = 69 + ( 10752 / 384 )
97 = 69 + ( 21084 / 753 )
97 = 70 + ( 26541 / 983 )
97 = 73 + ( 14592 / 608 )
97 = 73 + ( 21504 / 896 )
97 = 93 + ( 5628 / 1407 )
97 = 94 + ( 5208 / 1736 )
————–
98 = 4 + ( 96538 / 1027 )
98 = 10 + ( 82456 / 937 )
98 = 10 + ( 85624 / 973 )
98 = 12 + ( 74390 / 865 )
98 = 13 + ( 70465 / 829 )
98 = 15 + ( 74036 / 892 )
98 = 18 + ( 36720 / 459 )
98 = 18 + ( 37520 / 469 )
98 = 18 + ( 42960 / 537 )
98 = 18 + ( 46320 / 579 )
98 = 18 + ( 47360 / 592 )
98 = 18 + ( 53920 / 674 )
98 = 18 + ( 54320 / 679 )
98 = 18 + ( 59360 / 742 )
98 = 18 + ( 63520 / 794 )
98 = 18 + ( 74560 / 932 )
98 = 18 + ( 75360 / 942 )
98 = 18 + ( 76240 / 953 )
98 = 18 + ( 76320 / 954 )
98 = 20 + ( 61854 / 793 )
98 = 24 + ( 61790 / 835 )
98 = 25 + ( 68401 / 937 )
98 = 30 + ( 54128 / 796 )
98 = 40 + ( 51736 / 892 )
98 = 45 + ( 20617 / 389 )
98 = 45 + ( 32807 / 619 )
98 = 50 + ( 47136 / 982 )
98 = 51 + ( 37694 / 802 )
98 = 53 + ( 41760 / 928 )
98 = 54 + ( 13068 / 297 )
98 = 54 + ( 30712 / 698 )
98 = 56 + ( 12894 / 307 )
98 = 56 + ( 37842 / 901 )
98 = 60 + ( 19874 / 523 )
98 = 63 + ( 18970 / 542 )
98 = 63 + ( 24815 / 709 )
98 = 69 + ( 14732 / 508 )
98 = 70 + ( 14896 / 532 )
98 = 72 + ( 15834 / 609 )
98 = 75 + ( 13892 / 604 )
98 = 80 + ( 17352 / 964 )
98 = 93 + ( 7280 / 1456 )
98 = 93 + ( 7640 / 1528 )
98 = 93 + ( 7820 / 1564 )
98 = 93 + ( 8270 / 1654 )
98 = 95 + ( 7104 / 2368 )
98 = 96 + ( 2708 / 1354 )
98 = 96 + ( 2870 / 1435 )
98 = 96 + ( 3704 / 1852 )
98 = 96 + ( 4370 / 2185 )
98 = 96 + ( 7028 / 3514 )
98 = 96 + ( 7082 / 3541 )
98 = 96 + ( 8270 / 4135 )
98 = 96 + ( 8702 / 4351 )
————–
99 = 17 + ( 35096 / 428 )
99 = 24 + ( 60975 / 813 )
99 = 26 + ( 30587 / 419 )
99 = 36 + ( 58401 / 927 )
99 = 41 + ( 53708 / 926 )
99 = 45 + ( 16038 / 297 )
99 = 50 + ( 47138 / 962 )
99 = 54 + ( 17820 / 396 )
99 = 59 + ( 14720 / 368 )
99 = 63 + ( 17820 / 495 )
99 = 72 + ( 16038 / 594 )
99 = 95 + ( 7304 / 1826 )
————–
100 = 27 + ( 65043 / 891 )
100 = 36 + ( 57024 / 891 )
100 = 43 + ( 51072 / 896 )
100 = 45 + ( 21780 / 396 )
100 = 51 + ( 34692 / 708 )
100 = 72 + ( 13860 / 495 )
100 = 73 + ( 24516 / 908 )
100 = 82 + ( 10674 / 593 )


なお、今回の計算はEXCELに頑張ってもらいました。
参考までにvbaコードを掲載しておきます。
途中からセルではなくテキストファイルに書き出したため、セルへの出力はコメントアウトしています。

Option Explicit


Sub CentryPazzle()
Application.ScreenUpdating = False

Dim L As Integer ‘百の位
Dim datFile As String ‘書き出し用テキストファイル
Dim TryNO As Single ‘試す数字
Dim i As Integer
Dim BunBo As Long
Dim BunSi As Long
Dim SeiSu As Long
Dim AnsCo As Integer ‘該当する答えの数
‘Dim ColNO As Integer’セルに書き出しようの行ナンバー

datFile = ActiveWorkbook.Path & “\data.txt”
Open datFile For Output As #1

Cells.Clear

For L = 0 To 9 * L ‘1~100までを1000までに拡張するため

‘Cells(1 + 6 * L, 1) = “試す数”
‘Cells(1 + 6 * L, 2) = “”
‘Cells(1 + 6 * L, 3) = “整数”
‘Cells(1 + 6 * L, 4) = “分子”
‘Cells(1 + 6 * L, 5) = “分母”

‘ColNO = 2

For i = 1 To 100
TryNO = i + 100
AnsCo = 0

For SeiSu = 0 To TryNO – 1

If SeisuCheck(SeiSu) Then

BunBo = 1

Do
BunSi = (TryNO – SeiSu) * BunBo
If OneNineBoolean(SeiSu & BunSi & BunBo) = True Then
Print #1, TryNO & ” = ” & SeiSu & ” + ( ” & BunSi & ” / ” & BunBo & ” ) ”
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 1 + 6 * L) = TryNO
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 2 + 6 * L) = “=”
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 3 + 6 * L) = SeiSu
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 4 + 6 * L) = BunSi
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 5 + 6 * L) = BunBo
AnsCo = AnsCo + 1
End If

BunBo = BunBo + 1

Loop Until Len(SeiSu & BunSi & BunBo) > 10

End If

Next

If AnsCo = 0 Then
Print #1, TryNO & ” = 存在しない ”
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 1 + 6 * L) = TryNO
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 2 + 6 * L) = “=”
‘Cells(ColNO + 2 * (i – 1) + AnsCo, 3 + 6 * L) = “なし”
End If

Print #1, “————–”
‘ColNO = ColNO + AnsCo – 1
Next

Next

Close #1
Application.ScreenUpdating = True

End Sub


Function OneNineBoolean(mystr As String) As Boolean

Dim myBool As Boolean
myBool = True

Dim k As Integer
For k = 0 To 9
‘MsgBox (myStr & “/” & k & “/” & UBound(Split(myStr, CStr(k))))
If UBound(Split(mystr, CStr(k))) <> 1 Then
myBool = False
Exit For
End If
Next

OneNineBoolean = myBool

End Function


Function SeisuCheck(ByVal mystr As String) As Boolean

Dim ii, jj As Integer
Dim myBool As Boolean
myBool = True

For ii = 1 To Len(mystr)
If ii > 1 Then
For jj = 1 To ii – 1
If Mid(mystr, ii, 1) = Mid(mystr, jj, 1) Then
myBool = False
Exit Function
End If
Next
End If
Next

SeisuCheck = myBool

End Function


学習塾NextStage ( ネクストステージ )
■営業時間
平日13:00~21:30
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日曜 不定期
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■電話
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2017/03/19

北辰テスト(中2学力チェック号)で新たな発見!?

埼玉の県立入試が終えるとともに、新受験生となる中学校2年生を対象にした北辰テストが実施されました。

 

帳票が塾に届いて…生徒と話していると新たな発見が!?

 

4a4719b7a48b9efc9f8215ba7bd9035e_s


北辰テスト(中2学力チェック号)で新たな発見!?


その発見とは‥‥
作文の原稿用紙を逆さまに書くと…
点数がもらえません!!
知っていましたか?
くれぐれも、受験生は気を付けてください!!

「逆さまに書くわけねぇ~し…」と思っている受験生の皆さん…
馬鹿げた話かと思いきや、受験では思わぬことが起きるものです。
一つの教訓として、知っておきましょう!
個別相談会の評価に関わる北辰テストでなくて、本当に良かったです。
学習塾NextStage ( ネクストステージ )
■営業時間
平日13:00~21:30
土曜10:00~21:30
日曜 不定期
■住所
埼玉県川越市大字砂935-6
■電話
049-265-8994            

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