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Part of 2001 Singapore MO Open

Problems(1)

2001 golf balls which are numbered from 1 to 2001, a few in a box

Source: Singapore Open Math Olympiad 2001 2nd Round p3 SMO

4/2/2020
Suppose that there are 20012001 golf balls which are numbered from 11 to 20012001 respectively, and some of these golf balls are placed inside a box. It is known that the difference between the two numbers of any two golf balls inside the box is neither 55 nor 88. How many such golf balls the box can contain at most? Justify your answer.
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