Fewest Tokens: Pay 14
Read the puzzle
You must pay exactly 14 using tokens worth 1, 7 and 10. Each token can be used as many times as you like, and no change is given. Which tokens pay 14 with the fewest tokens?
Which tokens pay 14 with the fewest tokens?
Biggest first is not always fewest. Try every pair.
7 + 7
Just 2 tokens. Biggest first, 10 + 1 + 1 + 1 + 1, needs 5.
How to solve it
Test the smallest possible counts first.
One token: there is no 14 token, so that fails.
Two tokens: list the pairs. 10 + 10 = 20 (too much), 10 + 7 = 17 (too much), 10 + 1 = 11 (too little), 7 + 7 = 14 (exact), 7 + 1 = 8, 1 + 1 = 2. Only 7 + 7 lands on 14. So 2 tokens is the minimum: 7 + 7.
The usual wrong answer is 10 + 1 + 1 + 1 + 1. Taking the biggest token first leaves 4, and the only token small enough to fill 4 is the 1, so you need four of them. That pays 14 with 5 tokens, three more than the best answer.
Quick check: 7 × 2 = 14. Takeaway: when the biggest token leaves an awkward remainder, step back and try pairs of a middle token.
Learn the method: Coin Total Puzzles: Largest Unpayable Total and Fewest Tokens
