Q1.
Can you figure out which 5 cards add to 30? Is it possible? There are many ways of choosing 5 cards from this collection. Is there a way to find a solution without checking all possibilities?
Answer
It is not possible. No choice of 5 cards from that collection adds up to 30.
Look at the cards Kishor has: 13, 9, 1, 7, 11, 5 and 3 — every card carries an odd number.
odd + odd = even
(odd + odd) + odd = even + odd = odd
5 odd numbers = (odd + odd) + (odd + odd) + odd = even + even + odd = odd
30 is even, so the sum can never be 30.
(odd + odd) + odd = even + odd = odd
5 odd numbers = (odd + odd) + (odd + odd) + odd = even + even + odd = odd
30 is even, so the sum can never be 30.
Why it happens: you do not have to test the hundreds of choices. Odd numbers pair up two at a time to make even sums; with 5 cards one odd number is always left over, so the total is always odd.
Tip: if the target had been an odd number such as 31, it would be easy — for example 13 + 9 + 5 + 3 + 1 = 31.