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RMO Part -9

1)Let \(1<a_1<a_2<a_3<.....a_{51}<142\) for positive integers \(a_1,a_2,a_3,.....a_{51}\).

Prove that among the 50 consecutive differences some value must occur at least 12 times.

2)Prove that in any perfect square the three digits immediately to the left of the unit digit cannot be 101.

Try to solve these 2 problems in 1 hour.

Also try my set RMO.

Note by Naitik Sanghavi
1 year, 1 month ago

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Hints 1) Try Pigeonhole

2) Mods. Alan Yan · 1 year, 1 month ago

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