It wouldn't matter, they'd all hit the ground at the same time regardless of weight!I would just drop all coins together from the same height & see which one either hits the ground first or last.
How does this apply? If one of the coins was made of polystyrene and the rest of lead or vice versaIt wouldn't matter, they'd all hit the ground at the same time regardless of weight!
That's air resistance.How does this apply? If one of the coins was made of polystyrene and the rest of lead or vice versa
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.
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.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.
This was the start of one of my attempted solutions buy it can't work because -Put 6 coins on each side of scales, which ever side is heaviest contains the heavy coin...
... Find the odd coin and also whether it is lighter or heavier that the remaining 11...
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.
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!
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