MONEY for us all
Number Theory
Level
2
A country has three denominations of coins, worth 7, 10, and 53 units of value. What is the maximum number of units of currency which one cannot have if they are only carrying these three kinds of coins?
The answer is 46.
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1 solution
The largest value one is unable to make from 7 and 1 0 is 7 ∗ 1 0 − 1 0 − 7 = 5 3 , but there is a 5 3 -valued coin. One cannot make 4 6 either (if it were possible, one could make 4 6 + 7 = 5 3 ).
Checking the intermediary values:
From which we establish $46$ is the largest number.