Problema Solution
You have six canisters of the same size and shape. Five of these canisters contain exactly the same amount of gold, but the sixth one contains slightly more than the rest. If you are allowed to use a balance scale only twice, is it possible to determine the canister with the most gold? If yes, explain your procedure.
Answer provided by our tutors
Yes.
Lets denote the canisters with x1, x2, x3, x4, x5, x6
I divide the canisters in 3 groups of 2 canisters: (x1, x2), (x3, x4) and (x5, x6)
First i put on one side (x1, x2) and the other (x3, x4). we have the following cases
I) the scale is balancing
therefore the heavier canister must be in the (x5, x6) group
i use the balance scale Second time by putting x5 on one and x6 on the other side and find the heavier canister
II) the scale is not balancing
i select the heavier group, without using the generality we can say that is group (x1, x2)
i use the balance scale Second time by putting x1 on one and x2 on the other side and find the heavier canister