Question 8
A radio presenter invites listeners to “crack the code” to win a prize. The code is a four-digit number, which may start with a 0. All the digits are different and are arranged in ascending order, so 2457 is a possible code, but 1973 and 2448 are not. A caller guesses 0389 and is told that she has no number correct; a second then guesses 1456, and is told that she has three numbers correct and two of these are in the correct place. After this, the presenter giving a clue that this code is an even number. Is it now possible to “crack the code”, i.e. given these two guesses and the presenter’s responses, to give exactly one correct code fitting all the conditions. If not, why not?