You have five coins, apparently alike, but actually of different weights. You also have a two arm scale.

Can you manage to sort the coins in ascending order, using the scale only seven times?

Bonus question: can it be done in fewer weighings?

#1) Compare two coins; note which is heavier.

#2) Compare two other coins; note which is heavier.

#3) Compare the two "heavy" coins; note which is heavier. Now, you can label the four coins you have seen so far, so that A<B<D and C<D. We have now three coins in order.

#4) Compare the fifth coin ("E") to B.

#5) If E<B, compare E to A; otherwise, if E>B compare E to D. We will have either E<A<B<D, or A<E<B<D, or A<B<E<D, or A<B<D<E. We have now four coins in order.

#6) If there are three coins lighter than D, compare C to the middle one; if there are only two coins lighter than D, compare C to any one of them.

#7) Depending on the result of the previous weighing, comparing E to just one more coin, you'll have the five coins in order.

Posted by e.g. on 2004-05-31 15:31:28