New Scientist Enigma 570 – Dead Right
by Susan Denham
From Issue #1723, 30th June 1990
Two friends play a number game related to a popular board-game. Alan thinks of a secret four-figure number (that is, between 1000 and 9999) and Brian has to guess what it is. Each of Brian’s guesses is ‘marked’ by Alan who tells Brian how many of the digits are ‘dead-right’ (that is, correct and in the correct place) and how many others are ‘misplaced’ (that is, correct but in the wrong place). For example if the secret number were 4088 then the guess 4840 would get the marks ‘one dead-right, two misplaced’. Brian has to find the secret number with as few guesses as he can.
In a recent game Brian’s first few guesses and their ‘marks’ were:
First guess: 1234. One dead-right, one misplaced
Second guess: 1355. One dead-right, none misplaced.
Third guess: 1627. None dead-right, one misplaced.
For his fourth guess Brian chose the lowest number which could still be the secret number but it had none dead-right. I forget how many it had ‘misplaced’ but from the marks for the fourth guess Brian was able to work out what the secret number was.
What was it?