I have twelve £1 coins
One is defective in that it is either light or heavy but I don't know
which (remember that)
I have a set of simple balance scales (no weights)
I'm allowed to use the scales only 3 times
How do I find the defective coin ?
[I don't know the answer yet - sorry]
Martin
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That's a pretty old and good logic puzzle. To get you
started:
Arbitrarily number the balls from 1 thru 12. Then, for the
1st weigh, put balls 1-4 one side of the scale and balls 5-8 on the
other side.
If they balance, you know the odd ball is in the group 9-12.
In that case(they balance on weigh #1), put balls 1 & 9 on one side of
the scale and balls 10 & 11 on the other side.
If they balance again, the odd ball is #12. Weigh it against
any of the other balls to determine if it's heavier or lighter.
If they don't balance on weigh #2 and the side with ball #1 on
it goes down, then either the odd ball is #9 and it's heavier or the
odd ball is 10 or 11 and it's lighter. Weigh 10 against 11 to find
out. If they don't balance on weigh #2 and the side with ball #1 on
it goes up, either it's #9 and it's lighter or it's 10 or 11 and it's
heavier. Weigh 10 against 11 to find out.
Okay, that's the scoop for what to do IF the balls balance on
the 1st weigh. If they don't, it's more complicated and I'm too lazy
to type all that!!! Have fun!
