An arrangement machine reshuffles an input line by reversing a block of elements at the left end, one block per step. In Step 1 it reverses the order of the first two elements, in Step 2 the first three elements, in Step 3 the first four, and so on, each step reversing one element more than the step before. Nothing is added to or taken out of the line, and the machine stops after the step that reverses the whole line. Input: kite 48 lark 63 dome 29 fern. In Step 4 of the above arrangement, which element is third from the left end?

Question

Accepted Answer

kite. Step 1 (first two): 48 kite lark 63 dome 29 fern. Step 2 (first three): lark kite 48 63 dome 29 fern. Step 3 (first four): 63 48 kite lark dome 29 fern. Step 4 (first five): dome lark kite 48 63 29 fern. Counting from the left: dome, lark, kite — so kite is third. Stopping a place short gives lark, running a place past gives 48, and looking at the fifth place gives 63. Notice that kite happens to sit third in Step 3 as well as Step 4, but the elements around it are quite different.

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