An oldie but Goodie:

In front of you are 9 marbles and a balance (a scale that has two sides where you can weigh one side against the other). The marbles are all of identical size, and 8 of the 9 have an identical weight.

Using the balance, you need to find the odd-weight marble, and identify if it is heavier or lighter than the other 8 - but you can only use the balance 3 times.

How do you do it?

The solution, succinctly:

1. Split the 9 marbles into 3 groups of 3, call them A,B, and C

2. Weigh A vs B

3a. If A = B, the odd marble is in group C, Then weigh the three marbles in the group against each other, two will be equal, and you will know which is the odd one out, and if it's lighter or heavier.

3b. If A > B, then weigh A vs C; If A > C, you know that group A contains the marble, and it's heavier. If A = C, then group B contains the Marble and you know that the odd marble is lighter.

4. (Only if A<>B) - weigh two of the marbles in the "Odd" group, if they're equal, you know that the third marble is the odd one, and you've already established if it's lighter or heavier. If they're not equal, then the one on the side you've established is the odd one out.