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JoachimJo

10201 poker cases and 2 scales

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Hi, this is a riddle I just created. Sorry for my broken English, it's not my native language. There are two version of almost the same idea. The 1st one is purest, but the second one is more tricky. I think it's quite difficult to solve, but there is no need for any mathemical knowledge. 

First version of the riddle

A poker manufacturer has created 10201 cases each containing 100 chips. (Note: 10201=101*101)
10200 of these cases are perfect and each of their chips weighs 10g.
One of these cases is defective and its 100 chips weigh 11g each.

In order to determine which of the 10201 cases is defective, the manufacturer has two scales at his disposal:

  • A traditional, high-precision scale that can hold tons.
  • An electronic kitchen scale that displays the weight with a precision of 2g and can hold no more than 100g.

How can the manufacturer determine the defective case using only 2 times each of the 2 scales?

Second version of the riddle

A poker manufacturer has created 41010 cases each containing 100 chips. 
41009 of these cases are perfect and each of their chips weighs 10g.
One of these cases is defective and its 100 chips weigh 11g each.

In order to determine which of the 41010 cases is defective, the manufacturer has two scales at his disposal:

  • A traditional, high-precision scale that can hold tons.
  • An electronic kitchen scale that displays the weight with a precision of 1g and can hold no more than 100g.

How can the manufacturer determine the defective case using only 2 times each of the 2 scales?

 

balanceelectronique.jpg

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Edited by JoachimJo
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4 answers to this question

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I don’t see that I need the other scale.

Edited by CaptainEd
Oops wrong kind of scale, gotta remove my wrong answer

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For the second version, with the 1g precision scale, it is possible to go up to 41610 cases and not only 41010. I forgot one trick. :( sorry about that. 

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The kitchen scale: I’m trying to understand the 2g precision. Does that mean that if Ng is placed on it, it will display any number from N-1 to N+1 inclusive? Or N-2 through N+2? Or something else?

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