Problem 899. DistribuNim I

Two players play a game with two piles of stones. The players alternately take stones from one or both piles, subject to:

the total number of stones taken is equal to the size of the smallest pile before the move;
the move cannot take all the stones from a pile.

The player that is unable to move loses.

For example, if the piles are of sizes 3 and 5 then there are three possible moves.

(3, 5) \overset{(2, 1)}{\to} (1, 4) (3, 5) \overset{(1, 2)}{\to} (2, 3) (3, 5) \overset{(0, 3)}{\to} (3, 2)

$L(n)$ $(a,b)$ $1 \leq a,b \leq n$ $a$ $b$ is losing for the first player assuming optimal play.

$L(7) = 21$ $L(7^2) = 221$ .

$L(7^{17})$ .

两位玩家用两堆石子玩游戏，两人须在遵守如下规则的同时，轮流从一个石堆或者两个石堆中取石子：

首先无法操作的玩家落败。

例如，倘若初始时两个石堆各含 3、5 枚石子，那么此时先手有三种可行操作：

(3, 5) \overset{(2, 1)}{\to} (1, 4) (3, 5) \overset{(1, 2)}{\to} (2, 3) (3, 5) \overset{(0, 3)}{\to} (3, 2)

$L(n)$ $(a, b)$ $1 \leq a, b \leq n$ $a$ $b$ 枚石子，那么在两位玩家都以最优策略操作时，先手必败。

$L(7) = 21$ $L(7^2) = 221$ 。

$L(7^{17})$ 。

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