How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?(a) 14(b) 5(c) 9(d) 24This question was posed to me in a national level competition.The query is from Counting topic in chapter Counting of Discrete Mathematics

How many numbers must be selected from the set {1, 2, 3, 4} to guarant

1.	How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?(a) 14(b) 5(c) 9(d) 24This question was posed to me in a national level competition.The query is from Counting topic in chapter Counting of Discrete Mathematics
Answer» Right option is (b) 5 To elaborate: With 2 elements pairs which give sum as 7 = {(1,6), (2,5), (3,4), (4,3)}. So choosing 1 ELEMENT from each group = 4 elements (in worst case 4 elements will be either {1,2,3,4} or {6,5,4,3}). Now using pigeonhole principle = we NEED to choose 1 more element so that sum will definitely be 7. So NUMBER of elements must be 4 + 1 = 5.

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How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?(a) 14(b) 5(c) 9(d) 24This question was posed to me in a national level competition.The query is from Counting topic in chapter Counting of Discrete Mathematics

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