Mr. Letterman has an unlimited amount of 5-cent stamps and 7-cent stamps. What is the largest amount of postage that he cannot make?
To find the largest amount of postage that Mr. Letterman cannot make using 5-cent and 7-cent stamps, we can apply the "chicken McNugget theorem". According to this theorem, if two numbers, in this case 5 and 7, are relatively prime (have no common factors other than 1), the largest number that cannot be obtained by adding multiples of these two numbers is their product minus their sum.
In this case, the product of 5 and 7 is 5 * 7 = 35, and their sum is 5 + 7 = 12. Therefore, the largest amount of postage Mr. Letterman cannot make is 35 - 12 = 23 cents.