Respuesta :
Yes, One of them must be even and this is because Pigeonhole Principle.
What is Pigeonhole Principle?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
From series {1,2......2n}, we need to select 'n+1' integers.
Even integers series from above series is {2,4,6..........2(n-1), 2n}
Odd integers series from above series is {1,3,5......2(n-2), 2n-1}
We can choose only n odd integers from the series. Therefore, if we choose n+1 integers, at least one of them must have to be even integer.
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