hai guys
Divide coins into tree groups: group A contains coins 1, 2, 3, and 4; group B has coins 5, 6, 7, and 8; and group C, 9,10,11, and 12.
Weighing 1. Compare groups A and B.
If they are equal – all 8 coins are real.
Weighing 2. Compare 2 real coins with 9 and 10.
If they are equal – the fake coin is 11 or 12, if not – 9 or 10.
Weighing 3. Compare one of the two coins that can be fake with a real coin to find out whether it is fake.
If A is heavier than B, then coins in group C are real. The fake coin can either be in group A and be heavier than the others, or it can be in group B and lighter than the rest.
Weighing 2. Put coins 1, 2, 3, and 5 on one pan of the scales, and coins 4, 9, 10, and 11 on the other pan.
If they are equal, the fake coin is lighter and is either 6, 7, or 8 /Problem 1/.
If (1,2,3,5) is heavier, the fake coin is heavier and is either 1, 2, or 3 /Problem 1/.
If (1,2,3,5) is lighter, the fake coin is either 5 or 4 and we can find it by
Weighing 3. Compare coin 5 with any good coin /say, 12/.
If they are equal, 4 is the fake coin. Otherwise 5 is the fake coin.
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S.MOHAMED UVAIZ, B. Pharm.,
Dr.Agarwal's Eye Hospital
Kumbakonam.
09176250110
www.keralites.net |
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