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In a sports league, teams can either get 7 points or 3 points in each match. What is the largest score that cannot be attained?1. None of the above2. 223. 194. 115. 8

Question

In a sports league, teams can either get 7 points or 3 points in each match. What is the largest score that cannot be attained?1. None of the above2. 223. 194. 115. 8

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Solution

The largest score that cannot be attained in this sports league is 11.

Here's why:

This is a classic problem of number theory, known as the Chicken McNugget Theorem or the Frobenius Coin Problem. The theorem states that the largest number that cannot be expressed as a sum of multiples of two coprime (numbers with no common factors other than 1) numbers a and b is ab - a - b.

In this case, the two numbers are 7 and 3, which are coprime. So, the largest score that cannot be attained is 7*3 - 7 - 3 = 21 - 7 - 3 = 11.

So, the answer is 4. 11.

This problem has been solved

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