Question

given 8 different natural numbers, none greater than 15, show that at least three pairs of them have the same positive difference (the pairs need not be disjoint assets)

Answer 1

Answer:

2,3,5,7,9,11,13,15 are the answers

Answer 2

Step-by-step explanation:

Here the main observations are-

The selected numbers are Naturals numbers.

The count of selected numbers is more than 50% of total range( Here the range is 0–15)

Now Try proof by contradiction that none of the numbers have same +ve difference, you will find it is impossible. Simply go on for 1 pair, 2 pair and you will finally reach to your solution.