Combanotrics

Question

Consider a set {1,2,3.....,10} a pair of distinct number is selected again & again, atleast how many of these pair have same sum?

Comments

Total number of pairs possible is 10C2.

Now, sums which are possible in this scenario is min-- take pair (1,2) that is 3

And maximum take pair (9,10) that is 19 so sums which are possible are

3,4,5,6...........,18,19.

& 10C2 is 45.

So 45 is no. Of pigeons and (19-3+1) that is 17 are pigeonhole s so using pigeonhole principal we can say that atleast 3 of these pairs will have same sum.

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Yes what you have done its perfectly right but I want to know that atleast 3 pairs whose sum is same

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why 3...why not 2?

(1,5)

(2,4)

for sum 6 there are only 2 pairs