Set 5
Answer 7 |
Only 3 weighings are needed. Number the rings 1 to 10. Weighing 1: weigh 1,2,3 against 4,5,6 Weighing 2: weigh 1,2,3 against 7,8,9 There are 7 possible results: 1. [1,2,3] = [4,5,6] and [1,2,3] = [7,8,9] ; number 10 is odd. 2. [1,2,3] < [4,5,6] and [1,2,3] < [7,8,9] ; set [1,2,3] contains a lighter ring 3. [1,2,3] > [4,5,6] and [1,2,3] = [7,8,9] ; set [4,5,6] contains a lighter ring 4. [1,2,3] = [4,5,6] and [1,2,3] > [7,8,9] ; set [7,8,9] contains a lighter ring 5. [1,2,3] > [4,5,6] and [1,2,3] > [7,8,9] ; set [1,2,3] contains a heavier ring 6. [1,2,3] < [4,5,6] and [1,2,3] = [7,8,9] ; set [4,5,6] contains a heavier ring 7. [1,2,3] = [4,5,6] and [1,2,3] < [7,8,9] ; set [7,8,9] contains a heavier ring The 3rd weighing for result 1 is to weigh ring 10 against any one of the other rings to determine if it is lighter or heavier. The 3rd weighing for results 2 to 4 is to determine which of the 3 rings in the set is the light one. Weigh any one of the 3 rings against any other of the 3. If the two weigh the same then the 3rd is odd, otherwise the lighter one in the balance is odd. The 3rd weighing for results 5 to 6 is to determine which of the 3 rings in the set is the heavy one. Weigh any one of the 3 rings against any other of the 3. If the two weigh the same then the 3rd is odd, otherwise the heavier one in the balance is odd. | |
Freakish Facts |
63 year old Allan Todd has been dying up to seven times a day for 40 years. The sound of a door bell or telephone can cause him to have a seizure which stops his heart beating for up to 30 seconds. He has now been fitted with a pacemaker which restarts his heart after only 1.5 seconds. Romanian Nicolae Tabacu has been run over seven times in the 14 years from 1987 to 2001. The vehicles involved included cars, a bus, a motorcycle and a train. A boy in Romania tried to remove a marble that had become stuck in his younger brother's ear by pushing it with a pencil after his teacher had told him that "everything goes in one ear and out the other." 53 year old Wolfgang Kulov cycled 4 kilometres underwater along the German coastline in a record time of 3 hours, 15 minutes. During the journey, he had to swerve to avoid a garden gnome. |
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Ink Amera |
(C) David 2/9/2007 |
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