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Find the number of quintuples (x,y,z,u,v) of positive integers satisfying both equations `x+y+z+u= 100 and x+y+z+v= 70`

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RESONANCE-COMBINATORICS-Exercise-1 (Part-II RMO)
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  3. Find the number of 4 xx 4 array where entries are from the set {0,1,2,...

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  4. Find the number of 9 digit natural numbers in which each digit appears...

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  5. Find all 6-digit natural numbers a(1) a(2)a(3)a(4)a(5)a(6) formed by u...

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  6. Find number of three digit numbers equal to the sum of the factorials ...

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  7. Find the sum of all four digit numbers formed by the digits {1,2,3,….9...

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  8. Let n be a positive integer. Find the maximum number of non congruent ...

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  9. Find all the three digit numbers for which one obtains when dividing t...

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  10. Find all 8-digit numbers such that the sum of their digits is 14 and e...

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  11. Find all 7 digit numbers formed by using only the digits 5 and 7 and ...

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  12. Find the number of solution of the equation underset(l=1)overset(501)S...

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  13. The number of different seven-digit numbers that can be written usi...

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  15. Find the number of quintuples (x,y,z,u,v) of positive integers satisfy...

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