Doubt in math quiz pigenhole principle

#1

From the set of numbers s={1, 2, 3, 4}, how many minimum numbers must be selected to guarantee that at least one pair of these numbers has a sum equal to 7?

5

7

4

14

#2

@beastaman96
If it is possible to take multiple 1’s 2’s 3’s or 4’s
then, taking 2 any number of times will never give 7 as 2n != 7 for any n

Thus its now clear that you can take only once each number, taking n=1,2,3 would not guarantee 7 as sum
for n=3 one can select 1,2,3 (here no pair is summed to 7)
but n=4 guarantee
so go with 4

#3

to ensure that a pair has sum 7
the possible pair is 3,4
so if u select 1,2,3 then only if u next select 4 only then will a pair be generated such that sum is 7

so 4 is the answer ( 4 digits needs to be min chosen to get sum 7)

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#4

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