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Standard VIII

Mathematics

Subset

A subset B of...

Question

A subset B of the set of first 100 positive integers such that no two elements of B add up to 125. What is the maximum possible number of elements of B

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Solution

Maximum number of elements in B could be 62.
(1,2,3,4, ....................61,62,)
for every element x greater than 62 we have (125-x)
For example 63 +62 = 125
64 + 61 = 125
......................100+25 =125

Therefore (1,2,3,4, ....................61,62) would be the maximum subset.

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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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A subset B of the set of first 100 positive integers such that no two elements of B add up to 125. What is the maximum possible number of elements of B

Maximum number of elements in B could be 62. (1,2,3,4, ....................61,62,) for every element x greater than 62 we have (125-x) For example 63 +62 = 125 64 + 61 = 125 ......................100+25 =125 Therefore (1,2,3,4, ....................61,62) would be the maximum subset.

Maximum number of elements in B could be 62.
(1,2,3,4, ....................61,62,)
for every element x greater than 62 we have (125-x)
For example 63 +62 = 125
64 + 61 = 125
......................100+25 =125

Therefore (1,2,3,4, ....................61,62) would be the maximum subset.