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# 一題離散數學相關的問題

請問有沒有人可以幫我解答下列題目 感覺有點怪怪的

Let S = {3, 7, 11, 15, 19, ..., 95, 99, 103}. How many elements must we select from S to insure that will be at least two whose sum is 110?

我給一下他的選項 (a) 14 (b) 15 (c) 16 (d) 17

### 2 Answers

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- 六呎將軍Lv 71 decade agoFavorite Answer
First of all, let's find out all possible combination of 2 elements which gives a sum of 110:

7 + 103 = 110

11 + 99 = 110

.

.

51 + 59 = 110

A total of 12 pairs.

So in worst case, when 3 and 55 are also included (both of them cannot make a sum of 110 with any element in S), in addition to at least 13 of the above 12 pairs so that at least two of them should have a sum of 110, we have:

Min. no. of elements to be selected = 15

Source(s): Myself

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