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IMSO 2015 — Math Division — Essay Question 6

IMSO Maths · IMSO 2015 — Math Division — Essay

Question 6

There are 81 soldiers lined up in a row with numbers 1 to 81. In each of the rounds, the soldiers call out 1, 2, 3, 1, 2, 3, 1, 2, 3, .... All soldiers who count 1 and 3 are removed from the line. The process continues until only one soldier is left. What is the number of that last soldier left on the line?