問題の解答
検索用コード（LaTeX）
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% 例題A1.2.10：立体の色分け（One More）★★
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立方体の各面を，互いに異なる6色すべてを用いて互いに異なる色で塗り分ける方法は何通りあるか．ただし，立方体を回転させて面の色の配置が一致する場合は，同じ塗り方と見なすものとする．
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% 例題A1.2.10の解答（One More）★★
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あらかじめ1色を定め，その色の面を上面として固定する．
このとき，下面には残りの5色のうちの1色を用いるため，塗り方は，5通り
そのそれぞれについて，側面4面は異なる色を用いた円順列と考えられるから，
\[
(4-1)!=3!=6(\text{通り})
\]
よって，求める塗り分ける方法は，
\[
5\times 6=30(\text{通り})
\]
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% 問題A1.2.10：立体の色分け（One More）★★
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正四面体の各面を，互いに異なる4色すべてを用いて互いに異なる色で塗り分ける方法は何通りあるか．ただし，正四面体を回転させて面の色の配置が一致する場合は，同じ塗り方と見なすものとする．
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% 問題A1.2.10の解答（One More）★★
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あらかじめ1色を定め，その色の面を上面として固定する．
このとき，残りの側面には残りの3色を用いた円順列と考えられるから，
\[
(3-1)!=2!=2(\text{通り})
\]
よって，求める塗り分ける方法は，$2(\text{通り})$
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