SQLによる数独の解法
青山学院大学理工学部
矢吹太朗・佐久田博司
数独とは何か
• ナンプレとも呼ばれる
制約充足問題
• 各行・列・ブロックに1か
ら9の数字を一つずつ
当てはめる
• 新聞等に載っているも
のはとても簡単
• 人間には難しいもの→
もある
SQLで数独を解くことの意義
1. 非手続き的解法の優位性
– HowではなくWhatを記述すればよい
– 手続き的解法ではHowが必要
•
例：『プログラミング言語Ruby』（オライリー, 2009）
2. オプティマイザのベンチマーク
– オプティマイザの性質が、本解法に強く影響
– （結論：結合順序を最適化するべきではない）
非手続き的解法の優位性
手続き的解法と非手続き的解法
手続き的解法
非手続き的解法
問題 (What)
問題 (What)
手続き (How)
実行
実行
解
解
手続き的解法（容易な順）
• ネストしたfor文による全探索（非現実的）
– 非手続き的解法と同程度に単純
• 探索の枠組み
– 単純な{幅|深さ}優先探索
– Dancing Links: Knuth’s Algorithm Xの実装
• 数独に特化したアルゴリズム
ネストしたfor文（非現実的）
for (v12=1; v12<=9; v12++) {
for (v13=1; v13<=9; v13++) {
if (v12!=1 && v12!=2 && v12!=3
&& v12!=5 && v12!=7 && v12!=8
&& v13!=1 && v13!=3 && v13!=4
&& v13!=6 && v13!=7 && v13!=8
&& v13!=v12) {
print v12, v13;
}
}
}
ループ最深部のif文の
評価回数は、
空白が増えると
指数関数的に増加
&&
&&
&&
&&
v12!=4
v12!=9
v13!=5
v13!=9
ネストしたfor文（実行可能）
for (v12=1; v12<=9; v12++) {
if (v12についての条件) {
for (v13=1; v13<=9; v13++) {
if (v12!=v13 && v13についての条件) {
print v12, v13;
}
}
}
}
効率はよいが、
プログラムを書くのが面倒
SQLによる解法（実行可能）
SELECT v12, v13
FROM t12, t13
WHERE v12<>1 AND
AND v12<>5 AND
AND v13<>1 AND
AND v13<>6 AND
AND v12<>v13
v12<>2
v12<>7
v13<>3
v13<>7
AND
AND
AND
AND
v12<>3
v12<>8
v13<>4
v13<>8
非現実的なネストしたfor文
に似ているが、これは実行可能
AND
AND
AND
AND
v12<>4
v12<>9
v13<>5
v13<>9
非手続き的解法の優位性
ネストしたfor文（手続き的）
for (v12=1; v12<=9; …)
for (v13=1; v13<=9; …)
if (v12!=1 && …)
print v12, v13;
>>>このまま実行される
（非現実的）
SQL（非手続き的）
SELECT x.n AS v12, …
FROM x t12, x t13, …
WHERE v12<>1 AND …
>>>オプティマイザ
>>>実行プラン
>>>実行
□
オプティマイザのベンチマーク
最初の結果
RDBMS
実行時間
MySQL 5.1.41
1秒程度
PostgreSQL 8.4.2
測定不能
Oracle 11.1
31秒
SQL Server 2008 SP1
27秒
DB2 9.7 FP1
測定不能
Firebird 2.1.3
測定不能
Athlon X2 3800+, 主記憶1GB, Windows XP SP3 32bit
相違の原因：結合順序
• 空白1個にテーブル1個
が対応
• テーブルの結合順序が
重要
– 直接の関連があるもの
を結合させればよいはず
• 右はFROM句の記述通
りの結合順序
– 最適を目指すのは面倒
色の薄い部分に対応する
テーブルが先に結合
MySQLのテーブル結合順序
• FROM句の記述通りの
順番で結合
• テーブルにインデックス
があると、記述通りにな
らないことがある
• 安全のためには、
SELECT
STRAIGHT_JOIN …
色の薄い部分に対応する
テーブルが先に結合
PostgreSQLのテーブル結合順序
• 不適切な結合順序
– このままでは測定不能
• FROM句の記述通りの
順番で結合できるよう
に、コンマではなく
「CROSS JOIN」と書く
色の薄い部分に対応する
テーブルが先に結合
Oracleのテーブル結合順序
結合順序は適切
時間がかかりすぎる
最適化を止める
SELECT /*+ ORDERED */ …
SQL Serverのテーブル結合順序
結合順序は適切
最適化を止める
時間がかかりすぎる
SELECT … WHERE …
OPTION (FORCE ORDER)
DB2がダメな3つの理由
1. 結合順序が不適切
2. 結合方法が不適切
3. 条件が不適切な形に書き換えられる
v12<>1 AND v12<>2 → v12 NOT IN (1,2)
Firebirdがダメな理由
不明
結合順序についてのまとめ
RDBMS
結合順序の最適化
対策
MySQL 5.1.41
FROM句の記述通り
不要
PostgreSQL 8.4.2
誤り
最適化を止める
Oracle 11.1
時間がかかる
最適化を止める
SQL Server 2008 SP1
時間がかかる
最適化を止める
DB2 9.7 FP1
誤り
なし
Firebird 2.1.3
不明
なし
最終結果
RDBMS
最初の結果
最終結果
MySQL 5.1.41
1秒程度
1秒程度
PostgreSQL 8.4.2
測定不能
1秒程度
Oracle 11.1
31秒
1秒程度
SQL Server 2008 SP1
27秒
9秒
DB2 9.7 FP1
測定不能
測定不能
Firebird 2.1.3
測定不能
測定不能
□
SQLによる数独の解法のまとめ
1. 非手続き的解法の優位性
– HowではなくWhatを記述すればよい
2. オプティマイザのベンチマーク
– 結合順序を最適化するべきではない
•
•
•
•
MySQL：最適化していない（対策は不要）
PostgreSQL：誤った最適化（最適化を止める）
OracleとSQL Server：時間のかかる最適化（最適化を
やめる）
DB2とFirebirdでは本解法は利用できない
今後の展望
• 他のRDBMSについての調査
• 本解法の適用性のソースコードレベルでの議
論（オープンソースのRDBMSのみ）
• SQLで制約充足問題を解く一般的な方法の検
討
予備スライド
単純な{幅|深さ}優先探索
実は9x9の数独は簡単
1. 探索木を作る
–
–
親ノード：空白を1つ選択
子ノード：入りうる数を入れる
2. 単純な{幅|深さ}優先探索で
解ける
Mathematicaで約10行
数独に特化したアルゴリズムの例
• 数字の候補が一つしか
ないところを探す
• 例：7行8列は「8」
• 簡単な問題は、これを
繰り返すだけで解ける
• このようなアプローチは
数独では非推奨
SELECT t12.n AS v12,t13.n AS v13,t14.n AS v14,t15.n AS v15,t17.n AS v17,t19.n AS v19,t21.n AS v21,t23.n AS v23,t24.n AS v24,t26.n AS v26,t27.n AS v27,t28.n AS v28,t31.n AS v31,t32.n AS v32,t35.n AS v35,t36.n AS v36,t38.n AS v38,
t39.n AS v39,t41.n AS v41,t42.n AS v42,t45.n AS v45,t46.n AS v46,t48.n AS v48,t49.n AS v49,t51.n AS v51,t53.n AS v53,t54.n AS v54,t56.n AS v56,t57.n AS v57,t58.n AS v58,t62.n AS v62,t63.n AS v63,t64.n AS v64,t65.n AS v65,t67.n AS
v67,t68.n AS v68,t69.n AS v69,t72.n AS v72,t73.n AS v73,t74.n AS v74,t75.n AS v75,t76.n AS v76,t77.n AS v77,t79.n AS v79,t81.n AS v81,t83.n AS v83,t84.n AS v84,t85.n AS v85,t86.n AS v86,t87.n AS v87,t88.n AS v88,t91.n AS v91,t92.
n AS v92,t94.n AS v94,t95.n AS v95,t96.n AS v96,t98.n AS v98,t99.n AS v99 FROM x t12,x t13,x t14,x t15,x t17,x t19,x t21,x t23,x t24,x t26,x t27,x t28,x t31,x t32,x t35,x t36,x t38,x t39,x t41,x t42,x t45,x t46,x t48,x t49,x t51,x t53,x t54,
x t56,x t57,x t58,x t62,x t63,x t64,x t65,x t67,x t68,x t69,x t72,x t73,x t74,x t75,x t76,x t77,x t79,x t81,x t83,x t84,x t85,x t86,x t87,x t88,x t91,x t92,x t94,x t95,x t96,x t98,x t99 WHERE t12.n<>1 AND t13.n<>1 AND t14.n<>1 AND t15.n<>
1 AND t17.n<>1 AND t19.n<>1 AND t21.n<>1 AND t23.n<>1 AND t31.n<>1 AND t32.n<>1 AND t41.n<>1 AND t51.n<>1 AND t81.n<>1 AND t91.n<>1 AND t13.n<>t12.n AND t14.n<>t12.n AND t15.n<>t12.n AND t12.n<>7 AND t17.n<>
t12.n AND t12.n<>9 AND t19.n<>t12.n AND t21.n<>t12.n AND t12.n<>3 AND t23.n<>t12.n AND t31.n<>t12.n AND t32.n<>t12.n AND t42.n<>t12.n AND t62.n<>t12.n AND t72.n<>t12.n AND t12.n<>4 AND t92.n<>t12.n AND t14.n<>t
13.n AND t15.n<>t13.n AND t13.n<>7 AND t17.n<>t13.n AND t13.n<>9 AND t19.n<>t13.n AND t21.n<>t13.n AND t13.n<>3 AND t23.n<>t13.n AND t31.n<>t13.n AND t32.n<>t13.n AND t13.n<>5 AND t53.n<>t13.n AND t63.n<>t13.n
AND t73.n<>t13.n AND t83.n<>t13.n AND t15.n<>t14.n AND t14.n<>7 AND t17.n<>t14.n AND t14.n<>9 AND t19.n<>t14.n AND t24.n<>t14.n AND t14.n<>2 AND t26.n<>t14.n AND t14.n<>6 AND t35.n<>t14.n AND t36.n<>t14.n AND
t14.n<>3 AND t54.n<>t14.n AND t64.n<>t14.n AND t74.n<>t14.n AND t84.n<>t14.n AND t94.n<>t14.n AND t15.n<>7 AND t17.n<>t15.n AND t15.n<>9 AND t19.n<>t15.n AND t24.n<>t15.n AND t15.n<>2 AND t26.n<>t15.n AND t15.n
<>6 AND t35.n<>t15.n AND t36.n<>t15.n AND t45.n<>t15.n AND t15.n<>8 AND t65.n<>t15.n AND t75.n<>t15.n AND t85.n<>t15.n AND t95.n<>t15.n AND t17.n<>7 AND t19.n<>7 AND t24.n<>7 AND t26.n<>7 AND t35.n<>7 AND t36.
n<>7 AND t46.n<>7 AND t56.n<>7 AND t76.n<>7 AND t86.n<>7 AND t96.n<>7 AND t17.n<>9 AND t19.n<>t17.n AND t27.n<>t17.n AND t28.n<>t17.n AND t17.n<>8 AND t17.n<>5 AND t38.n<>t17.n AND t39.n<>t17.n AND t57.n<>t17.
n AND t67.n<>t17.n AND t77.n<>t17.n AND t87.n<>t17.n AND t17.n<>3 AND t19.n<>9 AND t27.n<>9 AND t28.n<>9 AND t38.n<>9 AND t39.n<>9 AND t48.n<>9 AND t58.n<>9 AND t68.n<>9 AND t88.n<>9 AND t98.n<>9 AND t27.n<>
t19.n AND t28.n<>t19.n AND t19.n<>8 AND t19.n<>5 AND t38.n<>t19.n AND t39.n<>t19.n AND t49.n<>t19.n AND t19.n<>2 AND t69.n<>t19.n AND t79.n<>t19.n AND t99.n<>t19.n AND t21.n<>3 AND t23.n<>t21.n AND t24.n<>t21.n
AND t21.n<>2 AND t26.n<>t21.n AND t27.n<>t21.n AND t28.n<>t21.n AND t21.n<>8 AND t31.n<>t21.n AND t32.n<>t21.n AND t21.n<>9 AND t41.n<>t21.n AND t51.n<>t21.n AND t21.n<>6 AND t81.n<>t21.n AND t91.n<>t21.n AND
t23.n<>3 AND t24.n<>3 AND t26.n<>3 AND t27.n<>3 AND t28.n<>3 AND t31.n<>3 AND t32.n<>3 AND t42.n<>3 AND t62.n<>3 AND t72.n<>3 AND t92.n<>3 AND t24.n<>t23.n AND t23.n<>2 AND t26.n<>t23.n AND t27.n<>t23.n AND
t28.n<>t23.n AND t23.n<>8 AND t31.n<>t23.n AND t32.n<>t23.n AND t23.n<>9 AND t23.n<>5 AND t53.n<>t23.n AND t63.n<>t23.n AND t73.n<>t23.n AND t83.n<>t23.n AND t23.n<>7 AND t24.n<>2 AND t26.n<>t24.n AND t27.n<>t2
4.n AND t28.n<>t24.n AND t24.n<>8 AND t24.n<>6 AND t35.n<>t24.n AND t36.n<>t24.n AND t54.n<>t24.n AND t64.n<>t24.n AND t74.n<>t24.n AND t84.n<>t24.n AND t94.n<>t24.n AND t26.n<>2 AND t27.n<>2 AND t28.n<>2 AND t
35.n<>2 AND t36.n<>2 AND t45.n<>2 AND t65.n<>2 AND t75.n<>2 AND t85.n<>2 AND t95.n<>2 AND t27.n<>t26.n AND t28.n<>t26.n AND t26.n<>8 AND t26.n<>6 AND t35.n<>t26.n AND t36.n<>t26.n AND t46.n<>t26.n AND t56.n<>
t26.n AND t26.n<>4 AND t76.n<>t26.n AND t86.n<>t26.n AND t96.n<>t26.n AND t28.n<>t27.n AND t27.n<>8 AND t27.n<>5 AND t38.n<>t27.n AND t39.n<>t27.n AND t57.n<>t27.n AND t67.n<>t27.n AND t77.n<>t27.n AND t87.n<>t
27.n AND t28.n<>8 AND t28.n<>5 AND t38.n<>t28.n AND t39.n<>t28.n AND t48.n<>t28.n AND t58.n<>t28.n AND t68.n<>t28.n AND t28.n<>1 AND t88.n<>t28.n AND t98.n<>t28.n AND t38.n<>8 AND t39.n<>8 AND t49.n<>8 AND t69.
n<>8 AND t79.n<>8 AND t99.n<>8 AND t32.n<>t31.n AND t31.n<>9 AND t31.n<>6 AND t35.n<>t31.n AND t36.n<>t31.n AND t31.n<>5 AND t38.n<>t31.n AND t39.n<>t31.n AND t41.n<>t31.n AND t51.n<>t31.n AND t81.n<>t31.n AN
D t91.n<>t31.n AND t32.n<>9 AND t32.n<>6 AND t35.n<>t32.n AND t36.n<>t32.n AND t32.n<>5 AND t38.n<>t32.n AND t39.n<>t32.n AND t42.n<>t32.n AND t62.n<>t32.n AND t72.n<>t32.n AND t32.n<>4 AND t92.n<>t32.n AND t35.
n<>9 AND t36.n<>9 AND t53.n<>9 AND t63.n<>9 AND t73.n<>9 AND t83.n<>9 AND t35.n<>6 AND t36.n<>6 AND t38.n<>6 AND t39.n<>6 AND t54.n<>6 AND t64.n<>6 AND t74.n<>6 AND t84.n<>6 AND t94.n<>6 AND t36.n<>t35.n A
ND t35.n<>5 AND t38.n<>t35.n AND t39.n<>t35.n AND t45.n<>t35.n AND t35.n<>8 AND t65.n<>t35.n AND t75.n<>t35.n AND t85.n<>t35.n AND t95.n<>t35.n AND t36.n<>5 AND t38.n<>t36.n AND t39.n<>t36.n AND t46.n<>t36.n AN
D t56.n<>t36.n AND t36.n<>4 AND t76.n<>t36.n AND t86.n<>t36.n AND t96.n<>t36.n AND t38.n<>5 AND t39.n<>5 AND t57.n<>5 AND t67.n<>5 AND t77.n<>5 AND t87.n<>5 AND t39.n<>t38.n AND t48.n<>t38.n AND t58.n<>t38.n A
ND t68.n<>t38.n AND t38.n<>1 AND t88.n<>t38.n AND t98.n<>t38.n AND t49.n<>t39.n AND t39.n<>2 AND t69.n<>t39.n AND t79.n<>t39.n AND t39.n<>7 AND t99.n<>t39.n AND t42.n<>t41.n AND t41.n<>5 AND t41.n<>3 AND t45.n
<>t41.n AND t46.n<>t41.n AND t41.n<>9 AND t48.n<>t41.n AND t49.n<>t41.n AND t51.n<>t41.n AND t53.n<>t41.n AND t41.n<>6 AND t62.n<>t41.n AND t63.n<>t41.n AND t81.n<>t41.n AND t91.n<>t41.n AND t42.n<>5 AND t45.n<
>t42.n AND t46.n<>t42.n AND t42.n<>9 AND t48.n<>t42.n AND t49.n<>t42.n AND t51.n<>t42.n AND t42.n<>1 AND t53.n<>t42.n AND t42.n<>6 AND t62.n<>t42.n AND t63.n<>t42.n AND t72.n<>t42.n AND t42.n<>4 AND t92.n<>t42.
n AND t45.n<>5 AND t46.n<>5 AND t48.n<>5 AND t49.n<>5 AND t51.n<>5 AND t53.n<>5 AND t62.n<>5 AND t63.n<>5 AND t73.n<>5 AND t83.n<>5 AND t45.n<>3 AND t46.n<>3 AND t48.n<>3 AND t49.n<>3 AND t54.n<>3 AND t56.n
<>3 AND t64.n<>3 AND t65.n<>3 AND t74.n<>3 AND t84.n<>3 AND t94.n<>3 AND t46.n<>t45.n AND t45.n<>9 AND t48.n<>t45.n AND t49.n<>t45.n AND t54.n<>t45.n AND t45.n<>8 AND t56.n<>t45.n AND t64.n<>t45.n AND t65.n<>
t45.n AND t45.n<>4 AND t75.n<>t45.n AND t85.n<>t45.n AND t95.n<>t45.n AND t46.n<>9 AND t48.n<>t46.n AND t49.n<>t46.n AND t54.n<>t46.n AND t46.n<>8 AND t56.n<>t46.n AND t64.n<>t46.n AND t65.n<>t46.n AND t46.n<>4
AND t76.n<>t46.n AND t86.n<>t46.n AND t96.n<>t46.n AND t49.n<>9 AND t57.n<>9 AND t67.n<>9 AND t69.n<>9 AND t77.n<>9 AND t87.n<>9 AND t49.n<>t48.n AND t57.n<>t48.n AND t58.n<>t48.n AND t48.n<>2 AND t67.n<>t48.
n AND t68.n<>t48.n AND t69.n<>t48.n AND t48.n<>1 AND t88.n<>t48.n AND t98.n<>t48.n AND t57.n<>t49.n AND t58.n<>t49.n AND t49.n<>2 AND t67.n<>t49.n AND t68.n<>t49.n AND t69.n<>t49.n AND t79.n<>t49.n AND t49.n<>7
AND t99.n<>t49.n AND t53.n<>t51.n AND t54.n<>t51.n AND t51.n<>8 AND t56.n<>t51.n AND t57.n<>t51.n AND t58.n<>t51.n AND t51.n<>2 AND t51.n<>6 AND t62.n<>t51.n AND t63.n<>t51.n AND t51.n<>3 AND t81.n<>t51.n AND
t91.n<>t51.n AND t53.n<>1 AND t54.n<>1 AND t56.n<>1 AND t57.n<>1 AND t58.n<>1 AND t62.n<>1 AND t63.n<>1 AND t72.n<>1 AND t92.n<>1 AND t54.n<>t53.n AND t53.n<>8 AND t56.n<>t53.n AND t57.n<>t53.n AND t58.n<>t53.
n AND t53.n<>2 AND t53.n<>6 AND t62.n<>t53.n AND t63.n<>t53.n AND t73.n<>t53.n AND t83.n<>t53.n AND t53.n<>7 AND t54.n<>8 AND t56.n<>t54.n AND t57.n<>t54.n AND t58.n<>t54.n AND t54.n<>2 AND t64.n<>t54.n AND t6
5.n<>t54.n AND t54.n<>4 AND t74.n<>t54.n AND t84.n<>t54.n AND t94.n<>t54.n AND t56.n<>8 AND t57.n<>8 AND t58.n<>8 AND t64.n<>8 AND t65.n<>8 AND t75.n<>8 AND t85.n<>8 AND t95.n<>8 AND t57.n<>t56.n AND t58.n<>t
56.n AND t56.n<>2 AND t64.n<>t56.n AND t65.n<>t56.n AND t56.n<>4 AND t76.n<>t56.n AND t86.n<>t56.n AND t96.n<>t56.n AND t58.n<>t57.n AND t57.n<>2 AND t67.n<>t57.n AND t68.n<>t57.n AND t69.n<>t57.n AND t77.n<>t5
7.n AND t87.n<>t57.n AND t57.n<>3 AND t58.n<>2 AND t67.n<>t58.n AND t68.n<>t58.n AND t69.n<>t58.n AND t88.n<>t58.n AND t98.n<>t58.n AND t67.n<>2 AND t68.n<>2 AND t69.n<>2 AND t79.n<>2 AND t99.n<>2 AND t62.n<>6
AND t63.n<>6 AND t65.n<>6 AND t67.n<>6 AND t68.n<>6 AND t69.n<>6 AND t81.n<>6 AND t91.n<>6 AND t63.n<>t62.n AND t64.n<>t62.n AND t65.n<>t62.n AND t62.n<>4 AND t67.n<>t62.n AND t68.n<>t62.n AND t69.n<>t62.n AN
D t72.n<>t62.n AND t92.n<>t62.n AND t64.n<>t63.n AND t65.n<>t63.n AND t63.n<>4 AND t67.n<>t63.n AND t68.n<>t63.n AND t69.n<>t63.n AND t73.n<>t63.n AND t83.n<>t63.n AND t63.n<>7 AND t65.n<>t64.n AND t64.n<>4 AND
t67.n<>t64.n AND t68.n<>t64.n AND t69.n<>t64.n AND t74.n<>t64.n AND t84.n<>t64.n AND t94.n<>t64.n AND t65.n<>4 AND t67.n<>t65.n AND t68.n<>t65.n AND t69.n<>t65.n AND t75.n<>t65.n AND t85.n<>t65.n AND t95.n<>t65.
n AND t67.n<>4 AND t68.n<>4 AND t69.n<>4 AND t76.n<>4 AND t86.n<>4 AND t96.n<>4 AND t68.n<>t67.n AND t69.n<>t67.n AND t77.n<>t67.n AND t87.n<>t67.n AND t67.n<>3 AND t69.n<>t68.n AND t68.n<>1 AND t88.n<>t68.n
AND t98.n<>t68.n AND t79.n<>t69.n AND t69.n<>7 AND t99.n<>t69.n AND t73.n<>3 AND t75.n<>3 AND t76.n<>3 AND t77.n<>3 AND t79.n<>3 AND t81.n<>3 AND t83.n<>3 AND t91.n<>3 AND t73.n<>t72.n AND t74.n<>t72.n AND t7
5.n<>t72.n AND t76.n<>t72.n AND t77.n<>t72.n AND t79.n<>t72.n AND t81.n<>t72.n AND t72.n<>4 AND t83.n<>t72.n AND t91.n<>t72.n AND t92.n<>t72.n AND t72.n<>7 AND t74.n<>t73.n AND t75.n<>t73.n AND t76.n<>t73.n AND
t77.n<>t73.n AND t73.n<>1 AND t79.n<>t73.n AND t81.n<>t73.n AND t73.n<>4 AND t83.n<>t73.n AND t91.n<>t73.n AND t92.n<>t73.n AND t73.n<>7 AND t75.n<>t74.n AND t76.n<>t74.n AND t77.n<>t74.n AND t74.n<>1 AND t79.n
<>t74.n AND t84.n<>t74.n AND t85.n<>t74.n AND t86.n<>t74.n AND t94.n<>t74.n AND t95.n<>t74.n AND t96.n<>t74.n AND t76.n<>t75.n AND t77.n<>t75.n AND t75.n<>1 AND t79.n<>t75.n AND t84.n<>t75.n AND t85.n<>t75.n AN
D t86.n<>t75.n AND t94.n<>t75.n AND t95.n<>t75.n AND t96.n<>t75.n AND t77.n<>t76.n AND t76.n<>1 AND t79.n<>t76.n AND t84.n<>t76.n AND t85.n<>t76.n AND t86.n<>t76.n AND t94.n<>t76.n AND t95.n<>t76.n AND t96.n<>t7
6.n AND t77.n<>1 AND t79.n<>t77.n AND t87.n<>t77.n AND t88.n<>t77.n AND t77.n<>7 AND t98.n<>t77.n AND t99.n<>t77.n AND t79.n<>1 AND t87.n<>1 AND t88.n<>1 AND t98.n<>1 AND t99.n<>1 AND t87.n<>t79.n AND t88.n<>t
79.n AND t79.n<>7 AND t98.n<>t79.n AND t99.n<>t79.n AND t81.n<>4 AND t83.n<>t81.n AND t84.n<>t81.n AND t85.n<>t81.n AND t86.n<>t81.n AND t87.n<>t81.n AND t88.n<>t81.n AND t81.n<>7 AND t91.n<>t81.n AND t92.n<>t8
1.n AND t83.n<>4 AND t84.n<>4 AND t85.n<>4 AND t87.n<>4 AND t88.n<>4 AND t91.n<>4 AND t92.n<>4 AND t84.n<>t83.n AND t85.n<>t83.n AND t86.n<>t83.n AND t87.n<>t83.n AND t88.n<>t83.n AND t83.n<>7 AND t91.n<>t83.n
AND t92.n<>t83.n AND t85.n<>t84.n AND t86.n<>t84.n AND t87.n<>t84.n AND t88.n<>t84.n AND t84.n<>7 AND t94.n<>t84.n AND t95.n<>t84.n AND t96.n<>t84.n AND t86.n<>t85.n AND t87.n<>t85.n AND t88.n<>t85.n AND t85.n<
>7 AND t94.n<>t85.n AND t95.n<>t85.n AND t96.n<>t85.n AND t87.n<>t86.n AND t88.n<>t86.n AND t94.n<>t86.n AND t95.n<>t86.n AND t96.n<>t86.n AND t88.n<>t87.n AND t87.n<>7 AND t87.n<>3 AND t98.n<>t87.n AND t99.n<>
t87.n AND t88.n<>7 AND t88.n<>3 AND t98.n<>t88.n AND t99.n<>t88.n AND t98.n<>7 AND t99.n<>7 AND t92.n<>t91.n AND t91.n<>7 AND t94.n<>t91.n AND t95.n<>t91.n AND t96.n<>t91.n AND t98.n<>t91.n AND t99.n<>t91.n AN
D t92.n<>7 AND t94.n<>t92.n AND t95.n<>t92.n AND t96.n<>t92.n AND t98.n<>t92.n AND t99.n<>t92.n AND t94.n<>7 AND t95.n<>7 AND t95.n<>t94.n AND t96.n<>t94.n AND t98.n<>t94.n AND t99.n<>t94.n AND t96.n<>t95.n AND
t95.n<>3 AND t98.n<>t95.n AND t99.n<>t95.n AND t96.n<>3 AND t98.n<>t96.n AND t99.n<>t96.n AND t98.n<>3 AND t99.n<>3 AND t99.n<>t98.n;
約12000字
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