Tag Archives: Pigeon Hole

10 point inside a circle, British Olympiad, 1983

Posted on February 13, 2015 by Sumant Sumant

If points are chosen in a circle of diameter , prove that the distance between some pair of them is less than

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The Circle and the Annulus

Posted on February 7, 2015 by Sumant Sumant

Let be a circle of radius and annulus having inner radius cm and outer radius cm. Now suppose a set of points is selected inside . Prove that, no matter how the points of may be scattered over , the … Continue reading →

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Exact distance apart

Posted on February 6, 2015 by Sumant Sumant

Prove that if we choose digits from the set then there are two digits which are exactly distance apart. Let the digits be . Add to each digit we get or . As each is unique it means each is also … Continue reading →

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A surprising property of the integer 11

Posted on February 6, 2015 by Sumant Sumant

No matter which positive integer may be selected from , prove that you must choose some two that differ by , some two that differ by , some two that differ by , and some two that differ by , … Continue reading →

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Divisible numbers among 2n numbers when n+1 are chosen

Posted on January 3, 2015 by Sumant Sumant

Prove that if you choose numbers out of numbers then there will be two numbers one of which divides the other. We observe that there are even numbers and also odd numbers. Now any number between and can be written … Continue reading →

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Luis Posa Problem

Posted on January 3, 2015 by Sumant Sumant

Prove that if you choose any numbers out of then there will be at least two numbers that are relative prime to each other. Here we can create pigeon holes .The numbers in each pigeon hole are relative primes because … Continue reading →

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