One person comes up to another person beside his bike. "Can I use your bike?" he asks. The person by the bike replies, "Only if you figure out the combination to my bike lock, which is made up of 4 different numbers from 1 through 8. You can guess 3 numbers."

He guessed 1235, 4721, and 3862. All three were answered with "One number in the combination is in the wrong place, and another is in the right place. The other two aren't in the combination."

The guesser was puzzled and asked "Is the number divisible by 7?" The person with the bike answered this question and after thinking for a while, the guesser told him the combination. What is the combination?

(OH OH, Gamer, I just noticed your warning to everyone not to post...)

The matrix, reloaded:
Replace "Is the number divisible by 7?", by "Is the number divisible by 5?"

The combination is 7825

Explanation:

1235 (one of the guesses) has exactly one of its digits both correct in value and correct in position, vis-a-vis the true combination, Therefore, in the true combination, pos1=1 or pos2=2 or pos3=3 or pos4=5.

If pos1=1, then pos2=(3 or 5) or pos3=(2 or 5),
or pos4=(2 or 3), since 1235 also has a digit correct in value but wrong in position. The only number like this that is consistent with the other two guesses is 1763.

Similarly, if pos2=2, then pos1=(3 or 5) or
or pos3={1 or 5} or pos4={1 or 3}. I found no number like this that is consistent with the other two guesses.

If pos3=3, then pos1={2 or 5} or pos2={1 or 5} or pos4={1 or 2}, 7831 is the only number like this which is consistent with the other two guesses.

Lastly, if pos4=5, then pos1={2 or 3} or pos2={1 or 3} or pos3={1 or 2}. 7825 is the only number like this that is in keeping with the other two guesses.

So the potential combinations are:
1763, 7831, and 7825.

And when the guesser was told that the combination was indeed divisible by 5, he knew that the combination must be 7825.

:-)







Edited on November 18, 2003, 6:19 am

Posted by Dan on 2003-11-18 04:20:44