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Topic: 8 coins with two heavier coins (Read 510 times) |
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wonderful
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8 coins with two heavier coins
« on: Apr 24th, 2008, 4:39pm » |
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There are 8 coins. The two coins X, and Y are heavier. Using the standard two-arms balance scale determines X, Y by 5 weightings. Also, determine if X>Y, X=Y or X<Y.
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| « Last Edit: Apr 25th, 2008, 1:16pm by wonderful » |
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rmsgrey
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Re: 8 coins with two heavier coins
« Reply #1 on: Apr 25th, 2008, 3:50am » |
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on Apr 24th, 2008, 4:39pm, wonderful wrote:There are 8 coins. The two coins X, and Y are heavier. Using the standard two-arms balance scale determines X, Y by 4 weightings. Also, determine if X>Y, X=Y or X<Y.
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Assuming you don't already know which coins are X and Y to start with, how can you tell which is X and which is Y when you find the odd pair in order to tell which of the two is the heavier one?
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Grimbal
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Re: 8 coins with two heavier coins
« Reply #2 on: Apr 25th, 2008, 7:32am » |
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It could be you need to identify the 2 coins and tell which one is heavier or whether they are both of the same weight.
Now let's see. 2 coins in 8 is 28 possibilities. Times 3 for the 3 relative weights. So you have 84 cases to distinguish.
But 4 3-way measurements can identify at most 81 cases.
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wonderful
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Re: 8 coins with two heavier coins
« Reply #3 on: Apr 25th, 2008, 1:15pm » |
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Thanks guys. Grimbal's observation is correct. I have revised the question accordingly.
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