So, someone answer this one since now I know that to get pfers to answer, I can't write a key in the beginning! haha
5. You have 12 balls. All of them are identical except one, which is either heavier or lighter than the rest. The odd ball is either hollow while the rest are solid, or solid while the rest are hollow. You have a scale, and are permitted three weighings. Can you identify the odd ball, and determine whether it is hollow or solid?
This is missing a key factor as well. The scale isn't a regular scale, it's a balance scale. That is the only way this is possible.
I was leaning towards a weighing like this:
1,2,3,4 - 5,6,7,8
1,3,5,6 - 2,9,10,11
1,4,7,9 - 2,5,11,12
Depending on whether the scale shows group A to be heavier, lighter, or even with group B, a process of elimination should be possible to determine the odd ball out and whether it's lighter of heavier.
So, let's take ball 4 as being heavier than the others. Weighing 1 would mean that either one ball in group A is heavier, or one ball in group B is lighter (even though we know ball 4 is heavy). Weighing two will be even meaning balls 1,2,3,5,6,9,10,11 are the same weight, which means 4,7,8 is the odd ball and either 4 is heavier or 7,8 is lighter. Weighing 3 will mean group A is heavier, so that automatically means 4 is the odd ball and is heavier. If 7 was the odd ball and lighter last weighing would show group B as being heavier. If 8 was the odd ball and lighter, then the last 2 weighings would be even. I've tried a few variations, and I'm pretty sure this route will work. I've yet to find a discrepancy.
Although, I have to be honest, I've thought about this one before and kind of tried different routes. It's not like I just came up with this in a few minutes.
