3

Part of 2014 Turkey Junior National Olympiad

Problems(1)

2014 balls arranged around a circle.

Source: Turkey Junior MO 2014 Problem 3

2014

106

different colors,

19

of each color. Determine the least possible value of

n

so that no matter how these balls are arranged around a circle, one can choose

n

consecutive balls so that amongst them, there are

53

balls with different colors.

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