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?

First of all, either 1 is in the combo or 2 is in the combo. If both were, only 3 numbers could be in the combo and if neither was there would have to be at least 5 numbers in the combo. The same reasoning can be applied with 2 and 3.

So there are two scenarios to consider. 1 and 3 are in the combo and 2 isn't, or 2 is in the combo and 1 and 3 aren't.

For the first one: there are 2 choices. 1__3 and __31 because if the last spot isn't filled, the 2 in the last number will make the numbers impossible. 1__3 must be 1763 and the __31 must be 7831.

For the second one: 2__5, __25, because _25_ and 52__ is impossible because the 2 is in the other two combinations in another spot. __25 results in 7825 and 2__5 results in 2765.

Since 2765 is the only number divisible by 7 and the other 3 numbers aren't, the number must be divisible by 7 so the guesser could figure it out. This means the combination was 2765.

Comments: (
You must be logged in to post comments.)