356.Last Number Standing
★★★puzzlesCitadel
The numbers 1 to 1000 are arranged in order around a circle. Starting by deleting 1, you then delete every second remaining number as you go round and round — so 1, 3, 5 and so on go first — continuing to wrap around until only one number is left. Which number survives?
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After the first full lap only the even numbers remain, which is the same puzzle at half the size. Track what the doubling does to the survivor.
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