You have ten coins, but two are fake, and weigh a little less. How many times do you have to use a two arm scale, in order to pick out the two fakes?

This may be a little confusing so I'll try to keep it as best organized as I can.

First split into groups of 3, 3 and 4.

Next weigh 1 group of 3 vs the other. (First time)

If:

A***) both sides are even, then you may have one coin in each. Or both coins in the group of 4.

Split the 4 coins into 2 groups of 1 and 1 group of 2. Weigh both groups of 1 vs each other. (Second time) If one goes down, the other is fake.

Weigh the next 2 and you will have your result in 3 weighs.

If they are even. Take one coin off and place another on (Making sure to keep track of which you just took off and such). Weigh the next 2 coins. If one side goes down, the other side (and the coin that was weigh with it, or not weighed depending which tilts) is fake. (Third weigh).

Now your really unlucky. You know there is 1 in each of the other 2 piles of 3. You then split them into groups of 1 and weigh them 1v1 with 1 coin off. If it tilts, you have your fake. If not, its the coin not weighed. Do that twice for the result in 5 weighs.

B***) one pile of 3 goes down. You may have 1 coin in both the pile of 3 and the pile of 4, or both may be in the pile of 3.

Split the 4 coins into 2 groups of 1 and 1 group of 2(Like the other way). Weigh the group of 1 vs each other. (Second time) If one goes down, the other is fake and you know that the last coin is in the group of 3.

Weigh the group of 3 1 v 1 and 1 off the scale to find the last (3 times and finished).

If the coins are equal, weigh the other 2 coins (Third time). Same as before, if one goes down continue to the group of 3 and finish it in 4 weighs. I

If the next 2 coins are equal, weigh one coin from each group. The side that tilts up will be fake, along with the coin it was with. (Finishing in 4).

Posted by Kardo on 2005-03-26 07:31:28