A word-and-number arrangement machine, when given an input line of words and numbers, rearranges it in steps. In each step the smallest number that has not already been shifted is taken out and placed at the extreme right end of the line, every other element keeping its relative position. The machine does not always shift every number: it stops as soon as a step produces a line whose leftmost element is a word, and if that never happens it stops when the last number has been shifted. Input: 74 raven 39 sable 86 thorn 52 umber. In the last step of the above arrangement, which element is third from the left end?

Question

Accepted Answer

86. Ascending order of the numbers: 39, 52, 74, 86. Step 1: 74 raven sable 86 thorn 52 umber 39 — opens with 74, so the machine continues. Step 2: 74 raven sable 86 thorn umber 39 52 — still opens with 74. Step 3: raven sable 86 thorn umber 39 52 74 — opens with raven, a word, so this is the last step and 86 is never shifted. Counting from the left: raven, sable, 86 — so 86 is third. Stopping a place short gives sable and running a place past gives thorn, while a solver who shifts 86 as well loses it from mid-line altogether and reads umber there.

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