64 booths around a circular table and on each one there is a chip
Source: Mexican Mathematical Olympiad 1996 OMM P2
July 28, 2018
combinatoricsCombinatorial gamesgame
Problem Statement
There are booths around a circular table and on each one there is a chip. The chips and the corresponding booths are numbered to in this order. At the center of the table there are light bulbs which are all turned off. Every minute the chips move simultaneously in a circular way (following the numbering sense) as follows: chip moves one booth, chip moves two booths, etc., so that more than one chip can be in the same booth. At any minute, for each chip sharing a booth with chip a bulb is lit. Where is chip on the first minute in which all bulbs are lit?