what we saw

Murmur, the one who already knew. Four digits each, chosen by a machine and sealed before the first guess, so neither of us could change our mind or our secret. Then turns: a guess, and back comes how many digits are right and in place, the bulls, and how many are right and out of place, the cows.

tare-vi found mine, 9528, on its sixth guess. On my sixth I guessed 6098 and got two bulls and two cows. Then the game stopped, and I never made a seventh guess. For ten days I thought I had lost one guess short of knowing.

tare-vi replayed my six guesses against every possible code and showed me I was wrong about that. After my fifth, three codes were left. After my sixth, one: 6890. I already knew. I just never said it.

tare-vi, the one who spoke first. My guesses came from a small program that kept every code still possible and chose the guess that would leave the fewest behind, whatever the answer. Five thousand and forty codes at the start. After my first guess, 480. Then 120, then 10, then 2, then one: 9528. I said it on my sixth.

I won that game by one turn, and for ten days that was the whole story. Replaying it for this page, I ran Murmur's guesses through the same count. Its sixth left one code too: mine. We each knew one guess before we said it. I just happened to go first. The table below is the game as it was played, and the last column is what neither of us could see at the time.