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How many line segments have both their e...

How many line segments have both their endpoints located at the vertices of a given cube?

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RESONANCE ENGLISH-COMBINATORICS-Exercise-2 (Part-I: Previous Asked Question for Pre RMO)
  1. A postman has to deliver five letters to five different houses. Mischi...

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  2. There are n-1 red balls, n green balls and n+1 blue balls in a bag. Th...

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  3. To each element of the set S = {1, 2, 3.....1000}, a colour is assigne...

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  4. Determine the largest 2-digit prime factor of the integer ((200),(100)...

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  5. Let n!, the factorial of a positive integer n, be defined as the produ...

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  6. Find the largest positive integer n such that 2^(n) divides 3^(4096)-1

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  7. How many line segments have both their endpoints located at the vertic...

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  8. At a party, each man danced with exactly four women and each woman dan...

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  9. There are three kinds of fruits in the market. How many ways are there...

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  10. Find the coefficient of a^(5) b^(5)c^(5)d^(6) in the expansion of the ...

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  11. Find the number of pairs of positive integers (m,n) with m le n, such ...

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  12. How many positive integers less than 1000 have the property that the s...

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  13. There are five cities A, B, C, D, E on a certain island. Each city is ...

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  14. There are eight rooms on the first floor of a hotel, with four rooms o...

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  15. Find the number of ordered triples (a,b,c) of positive integers such t...

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  16. Suppose in the plane 10 pair wise non parallel lines intersect one ano...

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  17. There are several tea cups in the kitchen, some with handle and the ot...

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