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APMOPS 2017 Question 16

APMOPS · APMOPS 2017

Question 16

2017 students arrange themselves in a single file. In the first round of counting, they number themselves $1,2,3,1,2,3,1,2,\ldots$ from left to right. In the second round, they number themselves $1,2,3,4,5,1,2,3,4,5,1,2,\ldots$ from right to left. Find the number of students whose difference between their numbers in the first and second rounds is 1.