A word-and-number arrangement machine, when given an input line of words and numbers, rearranges it in steps. In each step the machine takes the leftmost number that it has not already dealt with, replaces that number by the sum of its digits, and places the result at the extreme right end of the line. Words are never moved and never changed, every other element keeps its relative position, and the machine stops once every number of the original line has been dealt with. Input: 76 hazel 43 ivy 91 kite. In the last step of the above arrangement, which element is fourth from the left end?

Question

Accepted Answer

13. Digit totals: 76 gives 13, 43 gives 7, 91 gives 10. Step 1: hazel 43 ivy 91 kite 13. Step 2: hazel ivy 91 kite 13 7. Step 3, the last: hazel ivy kite 13 7 10. Counting from the left: hazel, ivy, kite, 13 — so 13 is fourth. Stopping a place short gives kite, running a place past gives 7, and taking the very last element gives 10. Note that the three words close up into hazel ivy kite because the numbers between them have been carried away, not because the words themselves moved.

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