There are 10 plates in a row. There is one apple on each plate.
一排有 10 个盘子。每个盘子上都有一个苹果。
Thomas, the kangaroo, loves to jump. First he jumps onto the leftmost plate with the letter A.
袋鼠托马斯喜欢跳跃。首先，它跳到了最左边标有字母 A 的盘子上。
On each single jump after this, he either jumps forward two plates, or backwards three plates.
在此之后的每一次跳跃，他要么向前跳两块板，要么向后跳三块板。
(An example of the two possible jumps from one plate is shown with arrows in the picture.)（从一块板上可能做出的两种跳跃方式在图中用箭头标出。）
Thomas only jumps onto plates with an apple. If he jumps onto a plate, he collects the apple from it.
托马斯只跳到有苹果的盘子上。如果他跳到盘子上，就会从盘子里把苹果拿走。
Question:问题:
If Thomas collects all 10 apples, which apple does he collect last?
如果托马斯把 10 个苹果都收集起来，他最后收集的是第几个苹果？
Explanation 解释
The correct answer is: I (the second apple fromt he right)
正确答案是：I（从右数第二个苹果）
We number the plates from left to right from A to J. Then Thomas can collect all ten apples in the order A, B, C, D, E, F, G, H, I, J.
我们从左到右将盘子依次编号为 A 到 J。这样托马斯就可以按照 A、B、C、D、E、F、G、H、I、J 的顺序收集所有十个苹果。
This is the only sequence of jumps that allows Thomas to collect all the apples. Why? To begin, Thomas must jump on plates A, C and then E because otherwise he jumps to the left of the first plate. Next, he must jump to plate B because he can only get to plate B from plate E and he will not return to plate E later. The same kind of reasoning can be used to see that all the remaining jumps are also determined uniquely.
这是托马斯能收集到所有苹果的唯一跳跃顺序。为什么？首先，托马斯必须跳到 A、C 然后是 E 板上，否则他会跳到第一块板子的左边。接下来，他必须跳到 B 板上，因为他只能从 E 板跳到 B 板，而且之后不会再回到 E 板。同样的推理可以得出，所有剩余的跳跃也都唯一确定了。
Bebras新赛季备赛已开启，扫码领取Bebras真题资料⇓
欢迎咨询【Bebras专业辅导课程】
（Bebras每日一练部分展示）
