IMO 1978 LL TUR36

The integers 1 through 1000 are located on the circumference

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IMO 1978 LL TUR36

Origin: TUR

Problem

The integers 1 through 1000 are located on the circumference of a circle in natural order. Starting with 1, every fifteenth number (i.e., 1, 16, 31, . . .) is marked. The marking is continued until an already marked number is reached. How many of the numbers will be left unmarked?