Nodes fixed by a group reversal

A list of n=15n = 15 nodes, numbered 11 through 1515 in their starting order, is reversed in consecutive groups of k=3k = 3 (reverse nodes 1133, then 4466, and so on; 1515 divides evenly into 55 groups). After the reversal, how many nodes remain in the same position they started in?

Show hints (2)+
  1. Reversing an odd-length block leaves its middle element in place.
  2. Count the blocks (15/315/3), then one fixed node per odd block.

Answer

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5

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Asked at: Multi-Strategy Quant, Game-Based Aptitude

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