Some simple factorization
Level
2
Let A, M and C be non- negative integers such that A+M+C=12. What is the maximum value of AMC + AM + MC + CA. Note: The numbers A, M, and C are not necessarily distinct.
The answer is 112.
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1 solution
A + M + C = 1 2 1 2 divided by three terms = 4 ( 1 2 / 3 = 4 ) . Thus A M C + A M + M C + C A = ( 4 ∗ 4 ∗ 4 ) + ( 4 ∗ 4 ) + ( 4 ∗ 4 ) + ( 4 ∗ 4 ) = 6 4 + 1 6 + 1 6 + 1 6 = 6 4 + 4 8 = 1 1 2 Which basically means tha A=4, M=4 and C=4.