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Weighing problem again...


Go to solution Solved by plainglazed,

Question

You have 8 coins that all look exactly the same, two of them are fake,one of these two fake coins is 0.1gm more than a normal coin, whereas the second coin is 0.1 gm less than a normal coin.

With howmany weighings can you find them out using a balance scale?

Edited by wolfgang
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  • Solution

Label the coins 1-8. There are 56 possible combinations of the Heavy and Light coins. I think they can be determined in four weighings:

1) Compare 1,2 v 3,4
If equal then the fake coins are either 1,2 3,4 5,6 5,7 5,8 6,7 6,8 7,8 (16 combinations)
2) Compare 1,3 v 2,5
If equal then 1,2,3,4,5 are "normal" (label X)
3) Compare X v 6
4) Compare X v 7
If > then either 1H and 2L or 3H and 4L or 5L and one of 6H,7H,8H
3) Compare 4 V 5
If equal then 1H and 2L
If < then 3H and 4L
If > then 5L and one of 6H,7H,8H
4) Compare 6 v 7
If < then either 1L and 2H or 3L and 4H or 5H and one of 6L,7L,8L
3) Compare 4 v 5 as above
If > then the fake coins are either 1H or 2H and one of 3L,4L,5L,6L,7L,8L or 3L or 4L and one of 5H,6H,7H,8H (20 combinations)
2) Compare 3 v 4
If equal then 1H or 2H and one of 5L,6L,7L,8L
3) Compare 1,5 v 2,6
If equal then either 1H,5L or 2H,6L
4) Compare 1 v 2
If > then 1H and one of 6L,7L,8L,
4) Compare 6 v 7
If < then 2H and one of 6L,7L,8L
4) Compare 6 v 7
If > then 4L and one of 1H,2H,5H,6H,7H,8H
3) Compare 1,2 v 5,6
If equal then 8H
If > then either 1H or 2H
4) Compare 1 v 2
If < then either 5H or 6H
4) Compare 5 v 6
If < then 3L and one of 1H,2H,5H,6H,7H,8H
3) Compare 1,2 v 5,6 as above
If < then the fake coins are either 1L or 2L and one of 3H,4H,5H,6H,7H,8H or 3H or 4H and one of 5L,6L,7L,8L (20 combinations)
2) Compare 3 v 4 as above

Could have easily messed something up but seems four weighings should somehow work.

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but my first pass through to find both fakes, assuming that the balance scale simply tells you "heavier" or "lighter" and that you can't measure HOW MUCH heavier or lighter is 5 weighings...I have a couple different approaches using 5 weighings, but will look for fewer.

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but my first pass through to find both fakes, assuming that the balance scale simply tells you "heavier" or "lighter" and that you can't measure HOW MUCH heavier or lighter is 5 weighings...I have a couple different approaches using 5 weighings, but will look for fewer.

Presume it tells you "equals" as well.

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but my first pass through to find both fakes, assuming that the balance scale simply tells you "heavier" or "lighter" and that you can't measure HOW MUCH heavier or lighter is 5 weighings...I have a couple different approaches using 5 weighings, but will look for fewer.

Presume it tells you "equals" as well.

yes...equals..is also possible ;)

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