If you pick 8 integers from 1 to 10 inclusive with no repeat

If you pick 8 integers from 1 to 10 (inclusive), with no repeats, what

Solution

Solution : 3 pairs

Given :

Hint: Use the Pigeonhold Principle, considering 5 buckets that hold{1, 10}, {2, 9}, {3, 8}, {4, 7}, {5, 6}, and determine how many buckets will have more than one number assigned to them.

Solution :

Now, we choose one integer from each bucket.

So, we have to select three more integers to complete eight as per query.

So, we choose three integers frm remaining five integers in the bucket.

Therefore , we get minimum of 3 pairs of integers that will add to exactly 11.