Fewest Tokens: Pay 11
Read the puzzle
Four token types are available in unlimited supply: 1, 5, 6 and 9. You must pay exactly 11 with no change given. Which tokens pay 11 using the fewest tokens possible?
Which tokens pay 11 with the fewest tokens?
Biggest first is not always fewest. Try every pair.
5 + 6
Just 2 tokens. Biggest first, 9 + 1 + 1, needs 3.
How to solve it
Start by asking whether 1 token or 2 tokens can do it.
One token: no token is worth 11, so one fails.
Two tokens: try each token with the partner it would need. 9 needs 2, and there is no 2 token. 6 needs 5, and 6 + 5 = 11 works. 5 needs 6, the same pair. 1 needs 10, which does not exist. So the fewest is 2 tokens: 5 + 6.
The common wrong answer is 9 + 1 + 1. Taking the biggest token first (9) leaves 2, which only two 1s can cover, so it takes 3 tokens. It pays 11, but it is one token more than needed.
Quick check: 5 + 6 = 11, and since no single token equals 11, 2 tokens is the least possible. Takeaway: for each token, ask what partner it needs; if that partner exists, you have a 2-token answer.
Learn the method: Coin Total Puzzles: Largest Unpayable Total and Fewest Tokens
