Coins on a scale (ENG/RUS)
The problem has two parts, A and B.
A.
There are 9 coins on the table. 8 of them are real and identical, 1 is fake and is heavier. You have a balance scale and your job is to find the fake one. How would you do it, if you are only allowed to use the scale two times?

B.
There are 12 coins on the table. 11 of them are real and identical, 1 is fake and has a different weight. You have a balance scale and your job is to find the fake one. How would you do it, if you are only allowed to use the scale three times?

Russian version:

А. На столе находятся 9 монеток: 8 одинаковых и 1 фальшивая. Фальшивая монетка внешне идентична остальным, но тяжелее обычной монетки. Как найти фальшивую монетку с помощью чашечных весов, если разрешено сделать только два взвешивания?

Б. На столе находятся 12 монеток: 11 одинаковых и 1 фальшивая. Фальшивая монетка внешне идентична остальным, но отличается от обычной монетки по весу (неизвестно, тяжелее она или легче). Как найти фальшивую монетку с помощью чашечных весов, если разрешено сделать только три взвешивания?

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All comments: 4
Dmitry Molochko: Part A is the easy one.
Split all coins into 3 piles of 3 coins each. Put any two of the piles on a scales. The counterfeit coin is in the heavier pile or if scales are balanced the counterfeit is in the third pile.
Take the pile in question which contains three coins and put any two of the coins on a scales. The heavier one is the counterfeit or if scales are balanced the counterfeit is the one that left.
To solve Part B we can go from here
2010-02-09 16:19:34    
Armin Shamshiri: Congratulations to Dmitry Molochko
Good job.
2010-02-10 01:44:50    
Andrey Pack: easy
this was a very logical problem to solve. but some of your others make you think, like the island one.

thanks
2010-02-16 21:02:54    
Armin Shamshiri: to Igor Chamgoulov:
Later on I plan to mark problems according to their difficulty level (easy/hard or something like that), but for now they are all mixed together. Glad you like them.
2010-02-21 10:02:51    

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