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Problem 237

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Tours on a 4 x n playing board

Let T(n) be the number of tours over a 4 × n playing board such that:

• The tour starts in the top left corner.
• The tour consists of moves that are up, down, left, or right one square.
• The tour visits each square exactly once.
• The tour ends in the bottom left corner.

The diagram shows one tour over a 4 × 10 board:

T(10) is 2329. What is T(10¹²) modulo 10⁸?

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4 x n棋盘上的巡游

记T(n)是在4 × n棋盘上按如下方式巡游的总方式数：

• 巡游从左上角开始。
• 巡游的每一步可以向上、向下、向左或向右移动一格。
• 巡游经过每格恰好一次。
• 巡游在左下角结束。

下图展示了4 × 10棋盘上其中一种巡游方式：

已知T(10)为2329。T(10¹²)模10⁸取余是多少？

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