Code Breaker Strategy: Crack Four Symbols

What the two counts mean

Suppose the code is circle, square, triangle, diamond and you guess circle, circle, diamond, star.

• Exact: the first circle is in the right slot, so 1 exact.
• Near: the diamond is in the code but in another slot, so 1 near. The second circle does not count, because the code has only one circle and it is already matched. The star is not in the code.

The counts are 1 exact, 1 near. Note that the counts do not say which symbols were right. Working out which they were is the puzzle.

The opening guess

With no repeats (easy and medium days), the opener should use four different symbols. The reply then tells you how many of those four are in the code, which with five or six symbols in play narrows things sharply:

• Five symbols, four in the guess: the code uses four different symbols, so exactly one of the five is missing. If your guess gets exact + near = 4, the missing symbol is the one you did not guess; if it gets 3, the missing symbol is one of your four and the fifth symbol is in the code.
• Six symbols, four in the guess: exact + near tells you how many of the two unguessed symbols are in the code (4 − total).

On hard days (repeats allowed) a good opener uses two pairs, such as circle, circle, square, square. The totals then tell you about two symbols at once, and repeats are tested from the start.

The second guess: shift and swap

Having learned which symbols are probably in the code, the second guess should both test the unknown symbol and move the known ones. Shifting all four symbols one slot to the right is a classic second guess: the change in the exact count tells you about positions. Swapping two symbols tests whether either was in place. Avoid a second guess that keeps everything where it was except one symbol; it tests only that one change.

Keeping the candidate list

The reliable way to play is to keep a short list of codes still consistent with every reply, and to choose guesses that split the list. You do not need to write out every candidate; keep the facts instead: "symbols in: A, C and one of D/F; A not in slot 1 or 2; C in slot 3 or 4". Each fact is a constraint, and after three guesses there are usually two or three codes left. Then guess one of them: either it is right or its reply decides between the others.

A guess does not have to be a possible answer. Sometimes a guess you know is wrong splits the remaining candidates better than any candidate does. With eight tries you have room for one or two such probes.

Hard days: repeats

When symbols can repeat, the number of codes is much larger and the counts are trickier (two of the same symbol in your guess against one in the code gives at most one mark). Use pair openers (A A B B, then C C D D) to count how many of each symbol the code has, then place them. A reply of 2 exact, 0 near to A A B B means the code has an A in one of slots 1 or 2 and a B in one of slots 3 or 4, or two As or two Bs in the right places; the next guess, A B A B, separates those.

Common mistakes

1. Assuming the exact mark belongs to a particular symbol. The counts are anonymous; test which symbol earned them.
2. Changing one symbol per guess. It is slow. Change several and read the difference.
3. Forgetting the symbols you have ruled out. Keep a note; eight tries go quickly.
4. Guessing only possible answers. A deliberately wrong probe can be the quickest route.
5. Ignoring repeats on hard days. If a symbol's total never adds up, it may appear twice.

Glossary

• Exact: a symbol in the right slot.
• Near: a symbol that is in the code but in another slot.
• Candidate: a code consistent with every reply so far.
• Probe: a guess chosen for information rather than as an answer.
• Pair opener: a guess of two symbols twice each, used when repeats are allowed.