What is the greatest amount of postage you can not pay using only 7 and 11 cent stamps?
To find the greatest amount of postage you cannot pay using only 7 and 11 cent stamps, we can use a mathematical concept called the Frobenius coin problem.
The Frobenius coin problem aims to find the largest value, known as the Frobenius number, that cannot be achieved by combining different amounts from a given set of values using addition.
In this case, our set of values is {7, 11}, representing the denominations of the stamps. Thus, we need to find the largest amount of postage (Frobenius number) that cannot be formed by any combination of 7 cent and 11 cent stamps.
To solve this problem, we can use a formula based on the Frobenius number. The formula is given by:
Frobenius number = (a * b) - (a + b),
where a and b are the denominations of the stamps. In this case, a = 7 and b = 11.
Substituting the values, we have:
Frobenius number = (7 * 11) - (7 + 11)
= 77 - 18
= 59
Therefore, the greatest amount of postage you cannot pay using only 7 and 11 cent stamps is 59 cents.