In a wonderland, a dime, quarter, & half are upgraded to have values of 12, 27, & 52 cents respectively.
What is the largest amount of money (in cents) that can not be represented as the combination of these coins?
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Relevant wiki: Postage Stamp Problem / Chicken McNugget Theorem
According to Dr. Warm's theorem , since gcd(12, 27, 52) = 1 and 12|lcm(27, 52), we can apply a formula for the Frobenius number :
g ( 1 2 , 2 7 , 5 2 ) = l c m ( 1 2 , 2 7 ) + l c m ( 1 2 , 5 2 ) − 1 2 − 2 7 − 5 2
g ( 1 2 , 2 7 , 5 2 ) = 1 0 8 + 1 5 6 − 9 1 = 1 7 3
Thus, the maximum number that these coins can not combine to is 173 cents.