Brainteaser with coins. Please help!!!?
Monday, February 8th, 2010 at
1:06 pm
You have twelve coins, one of which is a counterfeit. You have a balance, but it’s not the kind of balance that you can measure things on, it only has two ends with a fulcrum
in the middle, in other words, it only tells you which end is heavier. You can use the scale three times to weigh things. You know that the counterfeit coin is either heavier or lighter than a normal coin, but you don’t know which. How do you find the counterfeit coin?
This is part of my homework, please be serious.
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Tagged with: Coins • counterfeit coin • fulcrum • homework • three times
Filed under: Trivia
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YOU JUST LOST THE GAME!
From where did you get that counterfeit coin.Huh? Wait I am calling the police.
I’d trade them in for paper money and not worry about it.
all 3 first answers had me lmfao!
use strings tied to opposite ends of a pencil
In three weighings (X, Y, and Z) determine which of 12 coins (A through L) is of different weight. The "–" represents the center of a balance or scale. When coin I is used in weighing Y2 and Z3, it could be I, J, K, or L.
1. Weighing X, ABCD — EFGH set aside I, J, K, and L
12. X balanced, weighing Y1, AI — JK set aside L
12a. X balanced, Y1 balanced, the odd coin is L and weight is determined by weighing L against any other coin
12a. X balanced, Y1 tilted, the odd coin is I, J, or K
12a3. Weighing Z1, J — K set aside I
12a3a. Z1 balanced, the odd coin is I and weight is determined by Y1
12a3b. Z1 tilted opposite Y1, the odd coin is J and weight is determined by Y1 or Z1
12a3c. Z1 tilted same as Y1, the odd coin is K and weight is determined by Y1 or Z1
12b. X tilted, weighing Y2, ABG — CEI set aside D, F, and H
12ba. X tilted, Y2 balanced, the odd coin is D, F, or H
12ba3. Weighing Z2, F — H set aside D
12ba3a. Z2 balanced, the odd coin is D and weight is determined by X
12ba3b. Z2 tilted opposite X, the odd coin is F and weight is determined by X or Z2
12ba3c. Z2 tilted same as X, the odd coin is H and weight is determined by X or Z2
12bb. X tilted, Y2 tilted opposite as X, the odd coin is C or G
12bb3. Weighing Z3, C — I set aside G
12bb3a. Z3 balanced, the odd coin is G and weight is determined by X or Y2
12bb3b. Z3 tilted, the odd coin is C and weight is determined by X, Y2, or Z3
12bc. X tilted, Y2 tilted same tilt as X, the odd coin is A, B, or E
12bc3. Weighing Z4, A — B set aside E
12bc3a. Z4 balanced, the odd coin is E and weight is determined by X or Y2
12bc3b. Z4 tilted opposite X and Y2, the odd coin is B and weight is determined by X, Y2, or Z4
12bc3c. Z4 tilted same as X and Y2, the odd coin is A and weight is determined by X, Y2, or Z4
You can only use the scale three times – first step is to number the coins from 1 to 12…in some way that doesn’t alter the weight.
Divide the coins into 3 stacks, each with four coins. Balance stack #1 (1234) against stack #2 (5678) – if they weigh the same, you know that the counterfeit coin is in stack #3 (9-10-11-12). In which case:
Take coins 1+2, which you know are good coins, and balance them against coins 9+10. If they balance, then the bad coin is either 11 or 12. If they don’t, then the bad coin is either 9 or 10.
This narrows down the bad coin to one of two, and with your third use of the scale you should be able to figure out which one is bad – balance 11 against 1, and if 11 is legit, then 12 is bad, or vice versa.
But what if Stack #1 (1234) didn’t balance with stack 2 (5678)? The bad coin could be any of the first 8 coins, and there are only 2 weighings left….
Let’s say that (1234) is heavier than (5678). Then either the bad coin is part of (1234) and is heavy, or part of (5678) and is light.
This time (2nd use of scale) we weigh:
(1 2 3
against (9 10 11 4) – knowing that 9,10,11 are good coins.
If the left pan is lighter, then either 8 is the fake and is light, or 4 is the fake and is heavy. With the 3rd use of the scale, weighing either 4 or 8 against a known good coin (9 10 or 11) would prove which one is the fake – if 4 balances, then 8 is fake, and if 8 balances, 4 is fake.
In the 2nd weighing, if (1-2-3-8) balances (9-10-11-4), then all of those coins are good, the fake is in (5 6 7) and is light. If (1-2-3-8) is heavier, than then the fake is in (1 2 3) and is heavy.
Either way, you should be able to take either (567) or (123), and with the final weighing, determine the fake coin – weigh 5 against 6 or 1 against 2. If 5 balances 6, the bad coin is #7. If 5 doesn’t balance 6, the lighter one is the bad coin. If 1 balances 2, the bad coin is #3, but if not, then the heavy coin is the bad one.