A subset b of the set of first 100 positive integers has the property that no two elements of b sum to 125. what is the maximum possible number of elements in b?
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Since n∈Bn∈B implies 125−n∉B125−n∉B, BB can contain at most one integer from each pair {n,125−n}{n,125−n}, n∈{25,…,62}n∈{25,…,62}. Therefore |B|≤(62–25+1)+24=62|B|≤(62–25+1)+24=62.
On the other hand, {1,2,3,…,62}{1,2,3,…,62} is a set with 6262 elements which meets the given requirement.
The maximum number of elements is 6262. ■
rashmirbt10:
6262 is 62
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the answer should be in 2 digits only
62 is the answer for ur question brainliest
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