Tuesday, December 01, 2009

Easier Than Yesterday

• There are 8 balls.
• 7 balls are the same, the 8th is slightly heavier than the rest.
• You also have a balance-scale (the one with a platform on either side) but it has no markings on it.
Using the scale twice, locate the ball that is heavier.

4 comments:

1. Put three balls on each side of the scale.
If they balance, compare the other two to find the heavier ball.

If one side is heavier, pick two balls from that side (keeping the third apart) and compare them.
If they're the same, the third is the heavier ball.
If one of them is heavier, that's the heavier ball.

2. Weigh 1234 vs 5678.
Suppose 1234 is heavier.

Now weigh 15 vs. 23.
If 15 are heavier, 1 is the heavy ball.
If they are even, 4 is the heavy ball.
If 23 are heavier, put one ball in each hand and the heaviest one is the heavy ball.

3. If you were allowed to use your hands, there would be no need for the scale in the first place!

I believe Charli has the correct solution, but I could be wrong...

4. I'm with Josh on this one. You could imagine the weight difference being slight enough that you couldn't measure it by hand. Or perhaps the balls themselves are cannon balls, and so you're not capable of holding them both up.

The answer: as Charli already said: Put 2 of the balls aside. Weigh 3 of the remaining balls against the other 3 remaining. If they are the same then weigh the 2 balls that you put aside to find out which of them is heavier. If, instead, one of the sets of 3 balls was heavier, put one of the balls from the heavier set aside. Weigh the remaining two balls from the set to find out which one is heavier. If they are equal then you know it is the 1 ball that you put aside.

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