Best Puzzle I ever Heard

S

SparkRite

Registered User
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Ok folks, just to lighten the atmosphere here on AAM.
No trick wording or question, simply logic..........

There are 12 coins, each identical in appearence.
One is of odd weight.
You have a balance.
You are allowed three uses of the balance.

Find the odd coin and also whether it is lighter or heavier that the remaining 11.



I remember "Time" magazine offer $1000 to the first correct answer about 20 years ago or so.

I know the answer, myself and my maths lecturer worked it out, but it took some time.
 
I was dreaming about this bleedin' thing last night, doing binary splits and other fancy dance routines. I'm knackered and it's only 9:25am. :(
 
If by balance, you mean something that looks like this: --/\--
(Rotten solution deleted)

(If a grand was on offer, I'd brute force the combinations to find the solution. Shouldn't take that long considering number of coins on each side of the scale should be equal)


+++ Update - think I have it now +++
Step One
Divide into four piles of three, A B C and D
Weigh A against B
Weigh B against C

If A, B and C are all the same, D should go to next step
If A is different to both B and C, note if it's lighter or heavier - Use A for next step (Do same for B and C)

Step two - three coins left from step one
Coins E, F and G
Weigh E against F, if the same, odd coin is G, otherwise it's the lighter or heaver (see above) or either E or F.
 
I would just drop all coins together from the same height & see which one either hits the ground first or last.
 
Welfarite said:
It wouldn't matter, they'd all hit the ground at the same time regardless of weight!
Click to expand...
How does this apply? If one of the coins was made of polystyrene and the rest of lead or vice versa :confused:
 
umop3p!sdn said:
If by balance, you mean something that looks like this: --/\--
(Rotten solution deleted)

(If a grand was on offer, I'd brute force the combinations to find the solution. Shouldn't take that long considering number of coins on each side of the scale should be equal)


+++ Update - think I have it now +++
Step One
Divide into four piles of three, A B C and D
Weigh A against B
Weigh B against C

If A, B and C are all the same, D should go to next step
If A is different to both B and C, note if it's lighter or heavier - Use A for next step (Do same for B and C)

Step two - three coins left from step one
Coins E, F and G
Weigh E against F, if the same, odd coin is G, otherwise it's the lighter or heaver (see above) or either E or F.
Click to expand...

Hi umop3p!sdn, I see you have put a bit of thought into that,but unfortunatly you are not correct, you have not covered ALL the variables.

BTW. You are correct, by balance I do mean this --/\--
 
Make these three weighing with 4 coins on each side. The result will be either BB(BothBalance) or UD(UpleftandDownright) or DU(DownleftandUpright)
1,2,3,4 V's 6,7,9,11 The result will be one of BB/UD/DU
2,5,8,11 V's 3,4,6,10 The result will be one of BB/UD/DU
5,4,11,12 V's 1,6,7,8 The result will be one of BB/UD/DU

Then refer to the list below..
Coin #1 Heavy: BB,UD,DU.
Coin #1 Light: BB,DU,UD.
Coin #2 Heavy: DU,BB,DU.
Coin #2 Light: UD,BB,UD.
Coin #3 Heavy: UD,BB,DU.
Coin #3 Light: DU,BB,UD.
Coin #4 Heavy: UD,DU,DU.
Coin #4 Light: DU,UD,UD.
Coin #5 Heavy: DU,DU,BB.
Coin #5 Light: UD,UD,BB.
Coin #6 Heavy: UD,UD,UD.
Coin #6 Light: DU,DU,DU.
Coin #7 Heavy: BB,UD,UD.
Coin #7 Light: BB,DU,DU.
Coin #8 Heavy: DU,UD,BB.
Coin #8 Light: UD,DU,BB.
Coin #9 Heavy: BB,BB,UD.
Coin #9 Light: BB,BB,DU.
Coin #10 Heavy: UD,BB,BB.
Coin #10 Light: DU,BB,BB.
Coin #11 Heavy: DU,DU,UD.
Coin #11 Light: UD,UD,DU.
Coin #12 Heavy: BB,DU,BB.
Coin #12 Light: BB,UD,BB.
So print off the list and carry it around with you in case you ever find yourself in that particular situation!;)
 
Put 6 coins on each side of scales, which ever side is heaviest contains the heavy coin.

Discard the other 6.

Put 3 coins on each side of scales, which ever side is heaviest contains the heavy coin.

Discard the other 3.

From the 3 remaining coins, place 1 on each side of scales. You will either see one side being heavier (ie thats the heavy coin) or both will be equal weight, in which case the heavy coin is the one not on the scales.
 
homeowner said:
Put 6 coins on each side of scales, which ever side is heaviest contains the heavy coin.

Discard the other 6.

Put 3 coins on each side of scales, which ever side is heaviest contains the heavy coin.

Discard the other 3.

From the 3 remaining coins, place 1 on each side of scales. You will either see one side being heavier (ie thats the heavy coin) or both will be equal weight, in which case the heavy coin is the one not on the scales.
Click to expand...
Brilliant except for one thing; you presume the coin is heavier; it may be lighter. The quest is to determine the 'odd' weighted coin and whether it is lighter of heavier than the others in 3 uses of the scales.
 
Welfarite said:
Brilliant except for one thing; you presume the coin is heavier; it may be lighter. The quest is to determine the 'odd' weighted coin and whether it is lighter of heavier than the others in 3 uses of the scales.
Click to expand...

Oops, i misread the question.....
 
I would say that Cruger's solution is probably the correct way of thinking although the solution actually posted is incorrect:

If Coin 1 is heavier or lighter then the first "weighing" would not balance
If Coin 12 is heavier or lighter then the last "weighing" would not balance
 
Cruger is not correct and is overly complex...........

At least I don't think it is, did my head in trying to follow it.....:eek:
 
Crugers said:
Make these three weighing with 4 coins on each side. The result will be either BB(BothBalance) or UD(UpleftandDownright) or DU(DownleftandUpright)
2,5,8,11 V's 3,4,6,10 The result will be one of BB/UD/DU
5,4,11,12 V's 1,6,7,8 The result will be one of BB/UD/DU
1,2,3,4 V's 6,7,9,11 The result will be one of BB/UD/DU

Then refer to the list below..
Coin #1 Heavy: BB,UD,DU.
Coin #1 Light: BB,DU,UD.
Coin #2 Heavy: DU,BB,DU.
Coin #2 Light: UD,BB,UD.
Coin #3 Heavy: UD,BB,DU.
Coin #3 Light: DU,BB,UD.
Coin #4 Heavy: UD,DU,DU.
Coin #4 Light: DU,UD,UD.
Coin #5 Heavy: DU,DU,BB.
Coin #5 Light: UD,UD,BB.
Coin #6 Heavy: UD,UD,UD.
Coin #6 Light: DU,DU,DU.
Coin #7 Heavy: BB,UD,UD.
Coin #7 Light: BB,DU,DU.
Coin #8 Heavy: DU,UD,BB.
Coin #8 Light: UD,DU,BB.
Coin #9 Heavy: BB,BB,UD.
Coin #9 Light: BB,BB,DU.
Coin #10 Heavy: UD,BB,BB.
Coin #10 Light: DU,BB,BB.
Coin #11 Heavy: DU,DU,UD.
Coin #11 Light: UD,UD,DU.
Coin #12 Heavy: BB,DU,BB.
Coin #12 Light: BB,UD,BB.
So print off the list and carry it around with you in case you ever find yourself in that particular situation!;)
Click to expand...

Apologies... Copy and paste from excel gave terrible visual results so I had to cut and paste piece by piece..
Got the order of the three weighings, out of order...
I think I've got it in the correct order this time...
(until someone tells me different... :eek:)
 
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