Question

School calculators are sold by one company only in packages of 11 and packages of 15. What is the largest number of calculators it is not possible to purchase without opening a package?

Answer 1

This is known as a Frobenius problem, which is solved using the formula xy − x – y, where x and y represent the respective frobenius numbers.

If the company sells calculators only in packages of 11 and packages of 15, then x=11 and y=15.

The largest number of calculators it is not possible to purchase without opening a package is thus calculated as follows:

(11x15) – 11 – 15

= 165 – 11 – 15

=165 – 26

=139


If the company sells calculators only in packages of 11 and packages of 15, the largest number of calculators it is not possible to purchase without opening a package is 139