<Dl> <Dd> 2. c) The three remaining coins balance . In this case you just need to weigh the remaining coin against any of the other 11 coins and this tells you whether it is heavier, lighter, or the same . </Dd> </Dl> <Dd> 2. c) The three remaining coins balance . In this case you just need to weigh the remaining coin against any of the other 11 coins and this tells you whether it is heavier, lighter, or the same . </Dd> <Dl> <Dd> If one considers the symmetry, the weigh - ins are selected from three overlapping sets, as demarcated by the blue, red and green boxes (e.g. top row against bottom four). </Dd> <Dd> By always placing the "square group" on the same side of the scale and noting the balance (as well as any shift in balance between weigh - ins) the unique coin and its relative weight (heavier or lighter), can be deduced . </Dd> <Dd> If the first weigh - in balances, then the unique coin can be identified from the omitted four coins . <Ul> </Ul> </Dd> </Dl> <Dd> If one considers the symmetry, the weigh - ins are selected from three overlapping sets, as demarcated by the blue, red and green boxes (e.g. top row against bottom four). </Dd>

You are given 8 coins and a balance scale