Bulls and Cows
A three- or four-digit number is hidden, with no digit repeated. Each guess comes back as bulls and cows, and that is all you get to narrow it down. You have ten guesses; run out and the answer is revealed. The number is drawn inside your browser when the page opens, so not even the server knows it. The game is also called number baseball.
- No guesses yet.
Right digit in the right place is a bull; right digit in the wrong place is a cow. The answer never repeats a digit.
Spread the digits evenly over the first three guesses
The first guess can be anything. The trick is the second and third. Guess 123, 456 and 789 with no overlap and three guesses cover nine of the ten digits; whether 0 is in the answer follows from the three judgements added up. If the answer is 472, 123 comes back as one cow, 456 as one bull and 789 as one cow, which shows one digit in each group and no 0. From then on, only guess numbers that contradict none of the judgements so far. That method finishes both three and four digits within ten guesses.
The possible-answer count drops on an out as well
Three digits start at 720 possible answers. If the first guess is out, the answer can only use the seven remaining digits, so 7×6×5 = 210 remain. So an out is not a bad result — it erases three digits at once. Even when it reaches 1, which number it is remains yours to work out.
Records per digit count, today's board kept apart
The best is separate for three and four digits and changes only when a solved game took fewer guesses than the stored value. A game that used all ten is not a record. Today's board is drawn from the date, so everyone gets the same answer on the same day; it is always three digits and changes at midnight Korean time. Only the guess count of your first solved game that day is written down, and it never mixes into the best.
What this screen does not do
No time is measured. There are no hints; nothing beyond the possible-answer count is given away. The game is not stored, so a refresh draws a new answer, and the record stays in this browser only.
Common questions
QWhat counts as a bull and what as a cow?
Right digit in the right place is a bull; right digit in the wrong place is a cow. Neither means out. If the answer is 123 and you guess 321, only the 2 sits in its place — one bull, two cows.
QCan a digit appear twice?
No. The answer never repeats a digit and neither may your guess. Allowing repeats would force a ruling on cases like "two 1s, one of them right", and the rule stops fitting in a line. A leading zero is allowed, though — 012 is a valid answer.
QAre ten guesses enough?
Yes. Guessing any answer still consistent with the judgements so far solves all 720 three-digit and 5,040 four-digit answers, and the worst case is 9 guesses — averages of 5.27 and 5.56. Ten leaves one to spare.
QDoes the possible-answer count give it away?
No. It is computed from your guesses and their judgements alone, so it never states anything you could not derive on paper. It does the tedious part, not the deduction.
QIs four digits much harder than three?
Less than you would think. The possibilities go from 720 to 5,040, but each guess also tells you more — measured, the averages were 5.27 and 5.56 guesses, barely half a guess apart.
QDoes an invalid guess use up a try?
No. A wrong length or a repeated digit is bounced before judging and the tries left stay the same.
QWhat if I use all ten guesses on today's board?
The answer is shown and nothing is recorded, because only solved games count. A new game brings back the same answer, so you can try again — but the scoreboard is only yours to see, so solving it after seeing the answer fools no one but you.