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(402) 4

Part of 1994 Tournament Of Towns

Problems(1)

TOT 402 1994 Spring O J4 ten coins in a circle

Source:

6/12/2024
Ten coins are placed in a circle, showing “heads” (the tails are down). Two moves are allowed: (a) turn over four consecutively placed coins; (b) turn over four coins placed as XXOXXXX OXX (XX is one of the coins to be turned over, OO is not touched). Is it possible to have all ten coins showing “tails” after a finite sequence of such moves?
(A Tolpygo)
combinatorics