Fewest Tokens: Pay 18
Read the puzzle
Four token types are available in unlimited supply: 1, 4, 9 and 16 (the square numbers). You must pay exactly 18 with no change given. Which tokens pay 18 using the fewest tokens possible?
Which tokens pay 18 with the fewest tokens?
Biggest first is not always fewest. Try every pair.
9 + 9
Just 2 tokens. Biggest first, 16 + 1 + 1, needs 3.
How to solve it
Ask how few tokens could possibly work, and test each count in turn.
One token: none of 1, 4, 9 or 16 equals 18, so one is impossible.
Two tokens: try pairs that could reach 18. With a 16 you would need 2 more, and there is no 2 token. With a 9 you need 9 more, and 9 + 9 = 18 works. With only 4s and 1s, the biggest pair is 4 + 4 = 8, far too small. So the fewest is 2 tokens: 9 + 9.
The common wrong answer is 16 + 1 + 1, which is 3 tokens. It comes from the biggest-first habit: grab the 16, then cover the leftover 2 with two 1s. It reaches 18, but it is not the minimum.
Quick check: 9 + 9 = 18, and since one token cannot work, 2 is the least possible. Takeaway: the largest token is not always part of the best answer; try every pair before settling.
Learn the method: Coin Total Puzzles: Largest Unpayable Total and Fewest Tokens
