Sunday, July 24, 2005

12 pennies


This is an old one. You have 12 pennies. One is fake, either lighter or heavier than the others. You also have a balance scale. How can you determine which is the bad one in 3 weighings?

5 comments:

Anonymous said...

weigh 1, 2, 3, 10 vs. 4, 5, 6, 11
1, 2, 3, 11 vs. 7, 8, 9, 10
1, 4, 7, 10 vs. 2, 5, 8, 12

Blue said...

Once you you've done those weighings, how do you decide which is the bad coin?

Anonymous said...

each coin is in a unique group of weighings.

1 is in left, left, left
2 is in left, left, right
3 is in left, left, none
4 is in left, right, none
etc.

Also no opposite pattern to any of these is taken.

So if the scales tipped left, left, left you'd know 1 was heavier.
If it was the opposite, right, right, right, then 1 was lighter.

Anonymous said...

whoops, 4 is left, none, right.

Blue said...

Thanks. I guess Google knows everrything. Here are two sites that discuss this problem in detail. http://www.iwriteiam.nl/Ha12coins.html gives the answer above along with some others. http://www.cut-the-knot.com/blue/weight1.shtml gives other solutions.