Beavers love to play a game called "Strawberry Hunt."海狸们喜欢玩一个叫做“草莓狩猎”的游戏。
Rules: 规则:
- A different number of strawberries is put on each area of a field.在一块田地的不同区域放置了数量不等的草莓。
- Starting from any field, take 3 steps.从任何一块田地开始，走三步。
- Each step can be one of:每一步都可以是以下之一：
- move up one area 向上移动一个区域
- move down one area 向下移动一个区域
- move right one area 向右移动一个区域
- move left one area 向左移动一个区域
- Eat all the strawberries you found.把你找到的所有草莓都吃掉。
Examples:例子:
Choosing the path on the left, a beaver will eat 9 + 1 + 6 + 5 = 21 strawberries.
Choosing the path on the right, the beaver will eat 7 + 1 + 5 + 8 = 21 strawberries as well.
选择左边的路，一只海狸会吃掉 9 + 1 + 6 + 5 = 21 个草莓。选择右边的路，海狸也会吃掉 7 + 1 + 5 + 8 = 21 个草莓。
Little Beaver is playing on this grid:小海狸正在这个网格上玩耍：
Question:
How many strawberries can Little Beaver eat at most?小海狸最多能吃多少颗草莓？
Explanation 解释
Answer: 答案:23
Explanation: 解释:
Though there are 51 possible ways to finish the game (see table below), we don't have to check all 51 total sums of strawberries. Here is how:
尽管完成游戏有 51 种可能的方式（见下表），但我们不必检查所有 51 种草莓的总和。方法如下：
We know that each player can reach 4 areas that in their short path. These paths can only make the following shapes:
我们知道每个玩家在其短路径中可以到达 4 个区域。这些路径只能形成以下形状：
Now, we check these shapes including any of the areas with 9 or 8 strawberries (including all shapes with both of these areas). Since checking field combinations with 9 or 8 strawberries will also cover those fields with 5, 6 or 7 strawberries, all grids with larger numbers of strawberries will be covered. Then, we can find the largest total number of strawberries:
现在，我们检查这些形状，包括任何有 9 个或 8 个草莓的区域（包括所有同时具有这两种区域的形状）。由于检查有 9 个或 8 个草莓的田地组合也会涵盖那些有 5 个、6 个或 7 个草莓的田地，所以所有草莓数量更多的格子都会被涵盖。然后，我们就能找到草莓总数的最大值：
Now, note that without the areas with 8 and 9 strawberries, the maximum sum of strawberries on any other combination of four areas is 7 + 6 + 5 + 5 = 23. That is, also without areas 8 and 9, 23 cannot be exceeded. Therefore, Little Beaver can eat at most 23 strawberries.
现在请注意，如果没有 8 个和 9 个草莓的区域，那么其他任意四个区域的草莓总数最大为 7 + 6 + 5 + 5 = 23 个。也就是说，即便没有 8 个和 9 个草莓的区域，总数也无法超过 23 个。因此，小海狸最多能吃 23 个草莓。
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