CEMC Cayley

Algebra Difficulty 2.4 Junior Find the answer

Karim has 23 candies. He eats $n$ candies and divides the remaining candies equally among his three children so that each child gets an integer number of candies. Which of the following is not a possible value of $n$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

After Karim eats $n$ candies, he has $23-n$ candies remaining. Since he divides these candies equally among his three children, the integer $23-n$ must be a multiple of 3. If $n=2,5,11,14$ , we obtain $23-n=21,18,12,9$ , each of which is a multiple of 3. If $n=9$ , we obtain $23-n=14$ , which is not a multiple of 3. Therefore, $n$ cannot equal 9.

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