Best Puzzle I ever Heard

That's the answer but not the solution.

How do you determine which coins to weigh against which? 11,6 are weighed 3 times, 9,10 just once.

OK - how 'bout this

1. Weigh up coins (1-3) vs (4-6) - if they don't balance then go to step 2, if they do balance go to step 4

2. If the first 6 don't balance then select 3 new coins (7-9) and weigh up against 3 of the original 6 (1-3) - this will let you know if the odd-one out is in group (1-3) or (4-6) and also whether the coin is heavier or lighter

3. Once you know which group of 3 the coin is in you just take 2 of those 3 coins and weigh them up - if they balance it's the other one - if not you already know if the coin is heavier or lighter so it's obvious which it is.

4. If they balance, then the odd coin is in the group 7-12.

5. If 1-3 vs 7-9 doesn't balance then you know if the coin is heavier or lighter so select 7&8 and if they balance then 9 is the odd-one-out and if not then you know if it's 7 or 8

6. If 1-3 vs 7-9 balances then you know that the odd-one-out is 10-12 but you only have one weigh left so you're screwed!

AAAAAARRRRRRGGGGGGHHHHHH!!!!!!!!!!

Cruger, that seems to work out all right, but is not really practical.

How the hell did you work out which coins to weigh against which other coins??

Anybody want a little clue?

Weigh 4 coins against 4 coins.

A: If they balance, the odd one is one of the remaining 4. Weigh 3 of the remaining 4 against 3 known normal ones. If this balances, the only remaining unweighed coin is odd and can be tested against a normal to see if it is lighter or heavier. If this doesn’t balance, the odd is in the 3 recently weighed – and you’ll know if it heavier or lighter because the 3 are being weighed against normals. Weigh 2 of the 3 against each other to work out which of the three is odd.

B: If they don’t balance, remove three coins from the heavy side, replace with three coins from the light side. Put three known normals on the light side.
If thy balance, one of the 3 heavy side coins removed is a heavy coin – weigh two of them against each other to figure out which one.
If the side that was heavy is now light, one of the 3 coins moved from the light side to the heavy side is a light coin – weigh two of them to figure out which of the three.
If the heavy side stays heavy, EITHER the unmoved heavy side coin is heavy or the unmoved light side coin is light – test one of these against a known normal to find out which.

orka said:

Weigh 4 coins against 4 coins.

A: If they balance, the odd one is one of the remaining 4. Weigh 3 of the remaining 4 against 3 known normal ones. If this balances, the only remaining unweighed coin is odd and can be tested against a normal to see if it is lighter or heavier. If this doesn’t balance, the odd is in the 3 recently weighed – and you’ll know if it heavier or lighter because the 3 are being weighed against normals. Weigh 2 of the 3 against each other to work out which of the three is odd.

B: If they don’t balance, remove three coins from the heavy side, replace with three coins from the light side. Put three known normals on the light side.
If thy balance, one of the 3 heavy side coins removed is a heavy coin – weigh two of them against each other to figure out which one.
If the side that was heavy is now light, one of the 3 coins moved from the light side to the heavy side is a light coin – weigh two of them to figure out which of the three.
If the heavy side stays heavy, EITHER the unmoved heavy side coin is heavy or the unmoved light side coin is light – test one of these against a known normal to find out which.

Click to expand...

EXCELLENT, well done Orka.

The secret is in the second use of the balance, by transferring three from one side to the other,which is in fact giving you information about at least 9 coins and often also whether the odd one is heavier or lighter.

The easiest scenario is when the first use balances.

This is one of the puzzles conatined in the "Professor Layton and the Curious Village" game.

If you like this type of puzzle, you'll love this game- and its successor "Pandora's Box".

I was actually going to buy Pandora's Box for the DS last weekend but the puzzles featured on the front of the packaging looked very childish so I didn't bother in the end.