You are given twelve coins, of which eleven are genuine and one is fake. All eleven genuine coins have the same weight and the fake coin has a different weight. Find the fake in three weighings.
7 comments:
Anonymous
said...
Well, it's messy and complicated by the fact that we don't know whether the fake is light or heavy but bear with me.
Label the coins from A thru to L.
1. Weigh ABCD against EFGH.
a) If they balance then the fake coin is in IJKL; go to 2.
b) If ABCD is higher then either one of ABCD is fake and it's light OR one of EFGH is fake and it's heavy; go to 3.
c) If ABCD is lower then either one of ABCD is fake and it's heavy OR one of EFGH is fake and it's light; go to 4.
2. Weigh IJK against ABC (known to be not fake).
a) If they balance then L is fake. Weigh L against any other coin to see whether it's heavy or light.
b) If IJK is higher then the fake is one of IJK and it's light. Weigh I against J to see which is lighter. If neither then K is fake.
c) If IJK is lower then the fake is one of IJK and it's heavy. Weigh I against J to see which is heavier. If neither then K is fake.
3. IJKL are known to be not fake so weigh ABEF against CGIJ.
a) If they balance then the fake is either D (light) or H (heavy). Weigh DH against IJ. If DH is higher then D is the fake, otherwise H is the fake.
b) If ABEF is higher then either A or B are fake (and light) or G is fake (and heavy). Weigh A against G to see which it is. If neither then B is fake.
c) If ABEF is lower then either E or F are fake (and heavy) or C is fake (and light). Weigh E against C to see which it is. If neither then F is fake.
4. IJKL are known to be not fake so weigh ABEF against CGIJ.
a) If they balance then the fake is either D (heavy) or H (light). Weigh DH against IJ. If DH is higher then H is the fake, otherwise D is the fake.
b) If ABEF is higher then either E or F are fake (and light) or C is fake (and heavy). Weigh E against C to see which it is. If neither then F is fake.
c) If ABEF is lower then either A or B are fake (and heavy) or G is fake (and light). Weigh A against G to see which it is. If neither then B is fake.
You can't go to your step 2 because you don't know which 6 are "faulty". The puzzle doesn't tell you whether the fake coin is lighter or heavier than the rest so you are unable to decide which of the 6 from your first weighing contains the fake coin. That's why you have to use a more complicated system.
hey secret squirrel, i dun understand your (3rd and 4th) step B and C. if 1 is heavy and 1 is light then which is the fake 1? the heavy 1 or the light 1?
You don't have 1 heavy and 1 light at the same time. Those are just the possibilities which you are determining from the balancing.
In step 3b, if ABEF is higher then either one of A / B is fake and lighter (since they're higher) or G is fake and heavier (since it is lower). We arrived here from step 1b so we already knew that if EF were fake, they would be lower and if C was fake it would be higher. In this case I and J are known to be true.
Take 6 hangs in the balance and 6 in the balance the other, then take a lighter and Nksmanm 3 is at stake and 3 in the other. Then take lighter and take 2 of whom were put up all alone in the balance. We have either to be equal and, therefore, that we take is not fake or be one of the scales lighter.
7 comments:
Well, it's messy and complicated by the fact that we don't know whether the fake is light or heavy but bear with me.
Label the coins from A thru to L.
1. Weigh ABCD against EFGH.
a) If they balance then the fake coin is in IJKL; go to 2.
b) If ABCD is higher then either one of ABCD is fake and it's light OR one of EFGH is fake and it's heavy; go to 3.
c) If ABCD is lower then either one of ABCD is fake and it's heavy OR one of EFGH is fake and it's light; go to 4.
2. Weigh IJK against ABC (known to be not fake).
a) If they balance then L is fake. Weigh L against any other coin to see whether it's heavy or light.
b) If IJK is higher then the fake is one of IJK and it's light. Weigh I against J to see which is lighter. If neither then K is fake.
c) If IJK is lower then the fake is one of IJK and it's heavy. Weigh I against J to see which is heavier. If neither then K is fake.
3. IJKL are known to be not fake so weigh ABEF against CGIJ.
a) If they balance then the fake is either D (light) or H (heavy). Weigh DH against IJ. If DH is higher then D is the fake, otherwise H is the fake.
b) If ABEF is higher then either A or B are fake (and light) or G is fake (and heavy). Weigh A against G to see which it is. If neither then B is fake.
c) If ABEF is lower then either E or F are fake (and heavy) or C is fake (and light). Weigh E against C to see which it is. If neither then F is fake.
4. IJKL are known to be not fake so weigh ABEF against CGIJ.
a) If they balance then the fake is either D (heavy) or H (light). Weigh DH against IJ. If DH is higher then H is the fake, otherwise D is the fake.
b) If ABEF is higher then either E or F are fake (and light) or C is fake (and heavy). Weigh E against C to see which it is. If neither then F is fake.
c) If ABEF is lower then either A or B are fake (and heavy) or G is fake (and light). Weigh A against G to see which it is. If neither then B is fake.
1. 12--> 6|6
2.get 6(fault)--> 3|3
3.get 3(fault) --> 1|1 |1
either in first | second
@Anon
You can't go to your step 2 because you don't know which 6 are "faulty". The puzzle doesn't tell you whether the fake coin is lighter or heavier than the rest so you are unable to decide which of the 6 from your first weighing contains the fake coin. That's why you have to use a more complicated system.
hey secret squirrel,
i dun understand your (3rd and 4th) step B and C.
if 1 is heavy and 1 is light then which is the fake 1? the heavy 1 or the light 1?
You don't have 1 heavy and 1 light at the same time. Those are just the possibilities which you are determining from the balancing.
In step 3b, if ABEF is higher then either one of A / B is fake and lighter (since they're higher) or G is fake and heavier (since it is lower). We arrived here from step 1b so we already knew that if EF were fake, they would be lower and if C was fake it would be higher. In this case I and J are known to be true.
Take 6 hangs in the balance and 6 in the balance the other, then take a lighter and Nksmanm 3 is at stake and 3 in the other. Then take lighter and take 2 of whom were put up all alone in the balance. We have either to be equal and, therefore, that we take is not fake or be one of the scales lighter.
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