Let A={1, 2, 3, 4, 5, 6, 7, 8, 9} a) If five integers are selected from A, must at least one pair of the integer have a sume of 9?

Jaya Legge

Jaya Legge

Answered question

2020-12-29

Let A={1, 2, 3, 4, 5, 6, 7, 8, 9}
a) If five integers are selected from A, must at least one pair of the integer have a sume of 9?

Answer & Explanation

Mitchel Aguirre

Mitchel Aguirre

Skilled2020-12-30Added 94 answers

Given: A= {1,2,3,4,5,6,7,8,9}
Let us partition the set in the following five subsets:
{1,8}, {2,7}, {3,6}, {4.5}, {9}
Note that the sum of the distinct elements in each set sum up to 9.
If we then select 5 of the 9 integersin A, then it is possible to select 1 integer from each of the five subsets. When this occurs, then none of the pairs of integer will have a sum of 9 (as they can only have a sum of 9 when a pair falls in the same subset).

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