How do you find the irregular item using a balance and weighing the items only three times?

Question

You are given 12 apparently identical items, one of which is either heavier or lighter than the others whose weights are the same. Using a balance, what is a process you can use that will consistently find the irregular item and also determine whether it is heavier or lighter using the balance only three times?

Answer 1

If you are told whether the one is heavier or lighter you could:
separate into three groups of four.
Balance two of the groups:
If the groups balance the special one is in the last group
So take the last group and split into two pairs and Balance
Take the pair you know to be heavier or lighter from being told
and balance those two against each other to see which is the
heavier or lighter


If they don't balance:
Take the group you know to be heavier or lighter and do like I
said before and split into pairs and balance and then one on one.

However if it's unknown whether it's heavier or lighter it seems too difficult to only balance three times

Answer 2

ok.
weigh 2 of the objects. Record the weights.
If they are different, then weigh one more. The one of the two that is not equal is the irregular.

otherwise, put those two on one side of the scale.
put two new objects on the other side.

***If the amounts are unequal, weigh one of the two new objects.
the one that is different from the two original wieghts is the irregular.

if the amounts are the same, trash the two new objects and get two more BRAND new ones. Weigh the two BRAND new ones against the two originals. repeat from ***.


got it. You WILL hit an irregular one.

Answer 3

This is a classic interview question.

You can play this game interactively at
http://www.mapsofconsciousness.com/12coins/


See references below for solutions.