Author Topic: Riddle - you have 12 coins, one of which is counterfeit... (Read 6660 times)

MaterDominici · « **Reply #5 on:** July 02, 2016, 04:38:00 PM »

I've heard a similar version of this puzzle before.
I know the idea is to divide your possibilities into 3 groups, so you'd begin with 4 on each side of the scale and 4 off the scale.
From there, you hope that the scale balances as that would make things much easier! : )

Neil Obstat · « **Reply #6 on:** July 02, 2016, 06:55:49 PM »

Quote from: MaterDominici

I've heard a similar version of this puzzle before.
I know the idea is to divide your possibilities into 3 groups, so you'd begin with 4 on each side of the scale and 4 off the scale.
From there, you hope that the scale balances as that would make things much easier! : )

Yes, if it balances twice in a row, you end up with one lone coin that you know is counterfeit, and all you have to do for the 3rd turn is check it against a known good coin to see if the fake is heavier or lighter.

The trick is how to arrange coins for the second time at the scale. There are several possible scenarios.

Neil Obstat · « **Reply #7 on:** July 03, 2016, 10:49:55 AM »

The first variation in possible outcomes is the three categories of results for the first turn at the scale, namely, 1) Balances, 2) Left side goes up, 3) Right side goes up.

For each of these, there are at least 4 different possible locations for the fake coin. Your choice of what arrangement to use for the second turn must take all 12 of these possibilities into account.

JohnAnthonyMarie · « **Reply #8 on:** July 03, 2016, 01:33:53 PM »

ok, divide 12 coins into 3 Groups
Pass1: weigh two groups for 8known and 4unknown result (=4unknown)
Pass2: weigh 2known&2unknown vs 4known with 2unknown on side result (=2unknown)
Pass3: weigh 1known vs 1unknown with 1unknown on side result (=1unknown)

JohnAnthonyMarie · « **Reply #9 on:** July 03, 2016, 01:44:04 PM »

I'm not certain though. If pass one is equal I'm good. If pass one is not equal, I only know the third group weighs the same as one of the other two groups, but I really don't know which group. fun. good riddle.