Crack the Lock Riddle: Which 3-Digit Code Opens It? Answer: 738

The code is 738. The row with no marks rules out 2, 1 and 5. The gold dot for 132 then puts 3 in the middle, and the clues for 578 place 7 first and 8 last. The row for 672 confirms it.

How do you read the clues?

A gold dot means a digit is right and in the right place. A ring means a digit is right but in the wrong place. No mark means the digit is not in the code.

Work in this order:

1. 215 has no marks. So 2, 1 and 5 are not used.
2. 132 has one gold dot. The 1 and the 2 are out, so the 3 is right and already in place: the middle digit is 3.
3. 578 has one gold dot and one ring. The 5 is out, so 7 and 8 are both in the code. One is in the right place and one is not. The 7 cannot be in the middle, because 3 is there, so the 7 is the one in the wrong place and the 8 is right where it is: last.
4. That leaves the 7 for the first place, giving 738.
5. Check 672. The 7 is in the code but not in the middle, and the 6 and 2 are not used, so one ring is right.

What is the usual wrong answer?

A tempting wrong answer is 378. It comes from seeing that 3 and 7 are both in, but forgetting that the gold dot in 132 fixes the 3 in the middle.

Why do clue rows work so well?

Each clue row splits the possible codes into groups, the same way each weighing on a balance has only three results: left lighter, right lighter, or level ^[1]. Counting results like this sets a limit on how much a few weighings can tell you ^[1]. A 2020 paper calls a logic puzzle good when it has exactly one solution ^[2], and these four rows leave exactly one code.

Want to crack another one?

Each riddle below gives you a few clues and asks for a single answer.