2022-2023年Bebras挑战练习题-Pantry Map（储藏室地图）

Castorus found two good hiding places for his food.卡斯特鲁斯找到了两个藏食物的好地方。

He uses a map divided into squares to help him remember where his food is hidden. He wants to mark the squares, where his hiding places are, on his map with an X. However, if his rival Biberina finds the map, she would know where to look!他用一张划分成方格的地图来帮助自己记住食物藏在哪里。他想在地图上用 X 标出藏食物的地方所在的方格。然而，如果他的对手比贝里娜发现了这张地图，她就会知道该去哪里找！

Explanation 解释

Answer: 答案:

To find them, we look at the original map and find that there are two rows and two columns where the number of “X”s is not even: Rows 2 and 5 (from the bottom), and columns 3 and 5 (from the left).要找到它们，我们查看原始地图，发现有两行两列的“X”数量不是偶数：从下往上数的第 2 行和第 5 行，以及从左往右数的第 3 列和第 5 列。

This shows the rows and columns involved in yellow:这会将涉及的行和列以黄色显示：

The two erased “X”s showing the real hiding spots must have been in them! So we must find a way to add them back into these rows and columns to restore the even constraint.那两个被擦掉的表示真正藏匿点的“X”肯定就在其中！所以我们必须想办法把它们重新加回到这些行和列中，以恢复偶数约束条件。

There are 4 squares at the intersection of the yellow rows and columns. The upper red intersection square is marked with an “X” already: it cannot be a hiding place, since we know Castorus has erased the “X”s from the true hiding places. So in order to recover an even number of “X”s on that second row, we have to add it in the upper left yellow intersection square: we now know one hiding place.在黄色行和列的交叉处有 4 个方格。上面红色交叉方格已标有“X”：它不可能是藏匿处，因为我们知道卡斯特鲁斯已从真正的藏匿处擦掉了“X”。所以为了在第二行恢复偶数个“X”，我们得在左上角的黄色交叉方格加上一个“X”：现在我们知道了一个藏匿处。

The second hiding place can be determined as follows: Once we’ve found the first one, we cannot place the second one in the bottom left red intersection square, as this would result in 3 “X”s in the second column, and 3 is not even. The only choice left is the lower right intersection square, which gives the answer shown above.第二个藏匿点的确定方法如下：一旦我们找到了第一个藏匿点，就不能将第二个藏匿点放在左下角的红色交叉方格内，因为这样会导致第二列出现 3 个“X”，而 3 是奇数。唯一的选择就是右下角的交叉方格，这给出了上面所示的答案。

This shows the map before Castorus erased “X”s, with an even number of “X”s in each row and column:这展示了卡斯特鲁斯擦掉“X”之前的地图，每行和每列的“X”数量均为偶数：