counterfeit coin problem
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You are given 12 coins, one of which is counterfeit, and a balance pan scale. The fake coin is different in weight from the 11 genuine coins. Can you identify the counterfeit coin and whether it is heavier or lighter in 3 weighings?
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When I first read this puzzle from a book, it was 9 eggs and 2 tries, it has evolved much since then.
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Yah lor.....
I read it on "How to move Mt Fuji".
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can is can. but i dunno how do xD very complicated de.
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split into 6-6 the one with the fake coin is lighter. first try
split the portion with the fake coin into 3-3 and once again take the lighter side. second try
split any 2 out of the 3 coins. if the weighing scale is balance the odd coin is the fake, if its not the side of the scale which is lighter is the fake one. third try -
Originally posted by stellazio:
split the portion with the fake coin into 3-3 and once again take the lighter side. second tryAnd if the scale balances on your 2nd try due to the fact that the counterfeit coin is heavier then the rest?
What would you do for the 3rd try?
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Originally posted by Paradise Lost:
And if the scale balances on your 2nd try due to the fact that the counterfeit coin is heavier then the rest?
What would you do for the 3rd try?
if the counterfeit coin is heavier then the rest, then the side of 3 with the counterfeit coin will be heavier what.
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Originally posted by stellazio:
if the counterfeit coin is heavier then the rest, then the side of 3 with the counterfeit coin will be heavier what.
but the thing is u wont even know which is the counterfeit coin in the first place!
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Originally posted by jayh272416:
but the thing is u wont even know which is the counterfeit coin in the first place!
*facepalm -
Originally posted by jayh272416:
but the thing is u wont even know which is the counterfeit coin in the first place!you wont know until the 3rd step.
and its already stated that the counterfeit coin has a weight difference from the rest what.
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Originally posted by stellazio:
if the counterfeit coin is heavier then the rest, then the side of 3 with the counterfeit coin will be heavier what.
I think you misunderstood what I meant.
Your 1st try: 6 coins on each side, choose the lighter 6.
Your 2nd try: Split the lighter 6 into 2 pairs of 3 and weigh them. They will weigh the same IF the counterfeit coin is heavy AND is on the unchoosen other 6 from your 1st try.
Your now left with the other 6 coins with the knowledge that the counterfeit coin amongst then is heavy. What is your 3rd try?
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Originally posted by stellazio:
if the counterfeit coin is heavier then the rest, then the side of 3 with the counterfeit coin will be heavier what.
1st test, group A of 6(lighter) vs group B of 6.
2nd test, group A spilt into 2 groups of 3 you said.
And if the scale balanced on your 2nd try... then the counterfeit is in group B.
Pray tell what you do then to sieve the lone counterfeit from the 6 coins in group B in your only try left?
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I think you split 6 and 6. Then you shift 3 coins from left to right.
If the balance changes side. It means the fake coin is in the ones that u shifted.
If never change side, it means the fake coin is in the 3 that you never shift.
Then use stellazio's 3rd try lor.
Can right?
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should be do 5 5 first lah
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I got one method, don't even need to weigh.
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spilt the 12 coins into 3 groups of 4. A/B/C
Weight A against B.
Balanced then it is in group C, easy to discover.
2 tries to discover which of these 4 is counterfeit and heavier/lighter.
Remove C4. Test C1/C2 vs C3+geniune
Balanced = C4 counterfeit. weight to discover heavier/lighter.
Unbalanced... Remove C2 and weight C1+C3 vs 2 geniune
Balanced = C2 counterfeit. Recall tilt from 2nd try to know heavier/lighter.Unbalanced and tilt unchanged then it is C1. C1+C3 heavier = C1 heavier. Vice Versa
Unbalanced and tilt changed, then it is C3. C1+C3 heavier = C3 heavier. Vice Versa
Unbalanced then it is in group A or B.
Now we have A1/A2/A3/A4 and B1/B2/B3/B4 and KNOW which side is heavier/lighter.
Remove A1/A2 and B1 PLUS add a geniune C coin to A3/A4 AND switch A4 and B4 around (TRACK A4/B4)...
Now A1/A2/B1 is not on the scale. Keep TRACK of them regarding where they were from.
A3/B4/C against B2/B3/A4
If BALANCED then counterfeit is in A1/A2(LHS)/B1(RHS)
Remove A2. Move B1 to LHS and place 2 geniune on RHS.
If balanced, then it is A2. Recall tilt in try No.2
If unbalanced and tilt same way, then it is A1. Recall tilt in try No.2
If unbalanced and tilt changed, then it is B1. Use your common sense to know lighter/heavier.
If unbalanced and tilt unchanged, THEN it is either A3/B2/B3
Repeat above concept.
If unbalanced BUT tilt changed, THEN it is A4/B4
Replace A4 with geniune to weight against B4.
If balanced, B4 is geniune. Recall tilt from 2nd try to know A4 is heavier/lighter.
If unbalanced, B4 is counterfeit. See to know lighter/heavier.
Kindly point out any flaw if you see any flaw. Thanks.
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Originally posted by d3sT1nY:
I think you split 6 and 6. Then you shift 3 coins from left to right.
If the balance changes side. It means the fake coin is in the ones that u shifted.
If never change side, it means the fake coin is in the 3 that you never shift.
Then use stellazio's 3rd try lor.
Can right?
What if your 2nd try is balanced?
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Balanced then it is in group C, easy to discover.
2 tries to discover which of these 4 is counterfeit and heavier/lighter.
Remove C4. Test C1/C2 vs C3+geniune
Balanced = C4 counterfeit. weight to discover heavier/lighter.
Unbalanced... Remove C2 and weight C1+C3 vs 2 geniune
Balanced = C2 counterfeit. Recall tilt from 2nd try to know heavier/lighter.Unbalanced and tilt unchanged then it is C1. C1+C3 heavier = C1 heavier. Vice Versa
Unbalanced and tilt changed, then it is C3. C1+C3 heavier = C3 heavier. Vice Versa
ok, so the weighing of A and B is considered the first try, so the counterfeit is in C.
you remove C4 and you test C1/C2 vs C3+geniune? so is it C1+C2 or either C1/C2? -
Originally posted by stellazio:
Balanced then it is in group C, easy to discover.
2 tries to discover which of these 4 is counterfeit and heavier/lighter.
Remove C4. Test C1/C2 vs C3+geniune
Balanced = C4 counterfeit. weight to discover heavier/lighter.
Unbalanced... Remove C2 and weight C1+C3 vs 2 geniune
Balanced = C2 counterfeit. Recall tilt from 2nd try to know heavier/lighter.Unbalanced and tilt unchanged then it is C1. C1+C3 heavier = C1 heavier. Vice Versa
Unbalanced and tilt changed, then it is C3. C1+C3 heavier = C3 heavier. Vice Versa
ok, so the weighing of A and B is considered the first try, so the counterfeit is in C.
you remove C4 and you test C1/C2 vs C3+geniune? so is it C1+C2 or either C1/C2?Try No1. A and B balanced. Then counterfeit is either C1/C2/C3/C4
Remove C4.
LHS = C1+C3
RHS = C2+geniune coin
The above is the 2nd try.
If LHS = RHS, C4 is the counterfeit. Use 3rd try to determine heavier/lighter.
If LHS not equal RHS, Then counterfeit is either C1/C2/C3.
NOW REMOVE C2. PUT C1/C2 ON LHS. Put 2 genuine coins on RHS.
If tilt remain the same( eg. C1+C3 was heavier in 2nd try and C1+C2 is still heavier than the 2 genuine coins... then C1 is the counterfeit and it is heavier. Alternatively C1+C3 was lighter and still lighter... C1= lighter counterfeit)
If tilt change( eg C1+C3 was heavier in 2nd try and C1+C2 is NOW lighter than the 2 genuine coins... then C2 is the counterfeit and it is lighter. Alternatively, C1+C3 was lighter and NOW C1+C2 is heavier, thus C2 = heavier counterfeit).
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Originally posted by stellazio:
Balanced then it is in group C, easy to discover.
2 tries to discover which of these 4 is counterfeit and heavier/lighter.
Remove C4. Test C1/C2 vs C3+geniune
Balanced = C4 counterfeit. weight to discover heavier/lighter.
Unbalanced... Remove C2 and weight C1+C3 vs 2 geniune
Balanced = C2 counterfeit. Recall tilt from 2nd try to know heavier/lighter.Unbalanced and tilt unchanged then it is C1. C1+C3 heavier = C1 heavier. Vice Versa
Unbalanced and tilt changed, then it is C3. C1+C3 heavier = C3 heavier. Vice Versa
ok, so the weighing of A and B is considered the first try, so the counterfeit is in C.
you remove C4 and you test C1/C2 vs C3+geniune? so is it C1+C2 or either C1/C2?Try No1. A and B balanced. Then counterfeit is either C1/C2/C3/C4
Remove C4.
LHS = C1+C3
RHS = C2+geniune coin
The above is the 2nd try.
If LHS = RHS, C4 is the counterfeit. Use 3rd try to determine heavier/lighter.
If LHS not equal RHS, Then counterfeit is either C1/C2/C3.
NOW REMOVE C3. PUT C1/C2 ON LHS. Put 2 genuine coins on RHS.
If tilt remain the same( eg. C1+C3 was heavier in 2nd try and C1+C2 is still heavier than the 2 genuine coins... then C1 is the counterfeit and it is heavier. Alternatively C1+C3 was lighter and still lighter... C1= lighter counterfeit)
If tilt change( eg C1+C3 was heavier in 2nd try and C1+C2 is NOW lighter than the 2 genuine coins... then C2 is the counterfeit and it is lighter. Alternatively, C1+C3 was lighter and NOW C1+C2 is heavier, thus C2 = heavier counterfeit).
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Originally posted by Mikethm:
NOW REMOVE C2. PUT C1/C2 ON LHS. Put 2 genuine coins on RHS.
If tilt remain the same( eg. C1+C3 was heavier in 2nd try and C1+C2 is still heavier than the 2 genuine coins... then C1 is the counterfeit and it is heavier. Alternatively C1+C3 was lighter and still lighter... C1= lighter counterfeit)
If tilt change( eg C1+C3 was heavier in 2nd try and C1+C2 is NOW lighter than the 2 genuine coins... then C2 is the counterfeit and it is lighter. Alternatively, C1+C3 was lighter and NOW C1+C2 is heavier, thus C2 = heavier counterfeit).
im sorry, but actually i dont quite get this bit. so if lets say C4 is not the counterfeit, are you gonna remove anything from the scale first before your next step?
you remove C2, and you put either C1 or C2 on the LHS am i right? and on the other side you have 2 coins. but its already not balanced when its a 1v2 right?
actually 1 more question i have to ask is whether removing of coins counts as a try.
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Originally posted by stellazio:
im sorry, but actually i dont quite get this bit. so if lets say C4 is not the counterfeit, are you gonna remove anything from the scale first before your next step?
you remove C2, and you put either C1 or C2 on the LHS am i right? and on the other side you have 2 coins. but its already not balanced when its a 1v2 right?
actually 1 more question i have to ask is whether removing of coins counts as a try.
In my 1st try, I eliminated group A and B.
Before my 2nd try I know the counterfeit is in group C.
Either C1, C2, C3 or C4.
C4 is removed BEFORE try no.2.
Try No.2 consist of C1, C2, C3 AND 1 GENUINE coin from the 8 genuine coins I discovered in try No.1
I put C1+C3 on the left hand side AND C2 WITH the genuine coin on the RHS.
If C1+C3 balanced with C2+genuine coin, then C4 is the counterfeit.
Now if they don't balance, the counterfeit is either C1,C2 or C3.
PRETEND C1+C3 was heavier than C2+genuine on the 2ND TRY.
Now I remove C3 from the weighting and move C2 to the LHS. Put 2 geniune coins on the RHS.
NOW I have C1+C2 on the LHS and 2 geniune coins on the RHS.
PRETEND C1+C2 is lighter than the 2 genuine coins. THIS MEAN LHS was heavier on the 2nd try BUT lighter on the 3rd try. Since the scale tilt, IT MUST BE because the counterfeit SWITCHED sides.
Since C2 switched sides, C2 is the counterfeit.
Since C1(geniune)+C2(counterfeit) is lighter than 2 genuine coins, thus counterfeit is lighter.
I illustrated 1 situation to you. You can test the other situations.