Question

. 9. In a room there are 10 people, none of whom are older than 60 years (ages are given in whole numbers only )
but each of whom is at least 1 year old. Prove that one can always find two groups of people (with no common
person) such that the sum of ages of the people in each group is the same.
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Answer 1

There are two groups

sum of ages of each group is same

ages between 1year to 60 years

no repeation is allowed

they may be

group one is 10,25,30,40,50

total ages=10+25+30+40+50=155

second group is 5,15,35,45,55

whose sum=5+15+35-45+55=155