Question

You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more than the other side.

What is the smallest number of times you must use the scale in order to always find the fake coin?

Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale. etc.

These are modern coins, so the fake coin is not necessarily lighter.

Answer 1

hi maybe i can help

Answer 2

okay

Answer 3

Oh boy

Answer 4

I have tried to figure this out like 10 times and I cant get it

Answer 5

First I would divide into 3 sets with 4 coins in each. Label this A, B, and C. You can do four but it might be more confusing

Answer 6

So weigh each individual group (A, B, and C) and record how much each weighed. Whichever group is lighter, you know the coin is one of the four in the group. Lets suppose it was group C

Answer 7

Does that make sense so far?

Answer 8

yeah

Answer 9

Ok, so now you are going to weigh, individually, the coins in the group. Heres how it could go:

Measure 1st and second coin, which are the same weight. Measure third coin, it is different. Faulty coin. You should still weigh this coin so you know.

Measure 1st, 2nd, and 3rd coin, fourth one must be faulty.

In either, you should measure at least 3 coins. You can measure 4, but you don't have too.

Answer 10

So the least amount of times you had to use the scale would have been this:

Measure groups A, B, and C (3 times)
+
Measure 3 coins

So the least amount of times you had to use the scale would have to be 6 times.

Answer 11

Hope that helps :)

Answer 12

thank you

Answer 13

No problem :)