[Guest]

There are 12 coins, 11 equally heavy and one with a different weight (you don't know whether it's heavier or lighter).

How would you identify this coin with only a pair of scales which you may only use three times? You must also figure out whether this coin is heavier or lighter than the other coins.

Start by weighing 4 - 4.

-If the scale is balanced, weigh 3 of the remaining coins against three of the coins you already used.

+If the scale is balanced, weigh the last coin against a random coin to determen the deviation.

+If the scale is not balanced, weigh two of the three coins against each other.

>If the scale is balanced, it is the third coin

>If the scale is not balanced, you can use the information from the second weighing to figure out which coin is the distinct coin and whether it is heavier or lighter than the other coins.

-If the scale is not balanced, let's call the coins on the lower side 'l' and on the higher side 'h'. The coins we didn't use are called 'm'. Weigh llhhh - hmmmm.

+If the scale is balanced, weigh the remaining two 'lower' coins against each other.

>The lowered coin is the heavier coin.

+If the left side is lowered, weigh l - l.

>If the scale is balanced, the 'h' is the lighter coin.

>If the scale is not balanced, the lowered 'l' is the heavier coin.

+If the right side is lowered, weigh two of the three 'h'-coins from the left side against each other.

>If the scale is balanced, the third 'h'-coins from the left side is the lighter coin.

>If the scale is not balanced, the raised coin is the lighter coin.

[Guest]

i know this for certain

start by comparing coins 1-4 and 5-8

and i can solve the puzzle if the first weighing is equal, but not if one is heavier than the other. I'll have a think about that one and get back to ya

[bonanova]

There are 12 coins, 11 equally heavy and one with a different weight (you don't know whether it's heavier or lighter).

How would you identify this coin with only a pair of scales which you may only use three times? You must also figure out whether this coin is heavier or lighter than the other coins.

Start by weighing 4 - 4.

-If the scale is balanced, weigh 3 of the remaining coins against three of the coins you already used.

+If the scale is balanced, weigh the last coin against a random coin to determen the deviation.

+If the scale is not balanced, weigh two of the three coins against each other.

>If the scale is balanced, it is the third coin

>If the scale is not balanced, you can use the information from the second weighing to figure out which coin is the distinct coin and whether it is heavier or lighter than the other coins.

-If the scale is not balanced, let's call the coins on the lower side 'l' and on the higher side 'h'. The coins we didn't use are called 'm'. Weigh llhhh - hmmmm.

+If the scale is balanced, weigh the remaining two 'lower' coins against each other.

>The lowered coin is the heavier coin.

+If the left side is lowered, weigh l - l.

>If the scale is balanced, the 'h' is the lighter coin.

>If the scale is not balanced, the lowered 'l' is the heavier coin.

+If the right side is lowered, weigh two of the three 'h'-coins from the left side against each other.

>If the scale is balanced, the third 'h'-coins from the left side is the lighter coin.

>If the scale is not balanced, the raised coin is the lighter coin.

Hi lunkkun and welcome to the Den.

This is an old favorite that has already been posted here.

Use Search when posting puzzles you haven't created.

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