FILE No.84Unsolved
An old post office has only 3-cent and 5-cent stamps, in large numbers. There are no other stamps.
To post a letter you must make the postage exactly, using any number of these two stamps. For example, 8 cents is 3 + 5.
Some amounts cannot be made at all.
What is the largest amount that cannot be made?
If you get stuck, open the hints one at a time, in order.
Check amounts one by one from 1 cent.
What happens once three amounts in a row are possible?
Find the largest impossible amount.
What is the largest amount that cannot be made?
Choose the answer closest to the truth.
7 cents
The answer is: 7 cents.
Check amounts in order: 1 no, 2 no, 3 yes, 4 no, 5 yes, 6 yes (3+3), 7 no, 8 yes (3+5), 9 yes (3x3), 10 yes (5+5), 11 yes (3+3+5).
Once 8, 9 and 10 are possible, adding a 3-cent stamp gives 11, 12, 13, and so on, so everything from 8 up can be made. The largest impossible amount is 7.
People assume big amounts are fine and skip checking the small ones.
The cases on this site are fictional puzzles created for entertainment. Any resemblance to real people, organizations or events is coincidental.
© Unsolved Files
