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        riddles >> hard >> Coin weghting: 13 coins with  2 defected coins
        
(Message started by: wonderful on Apr 3^rd, 2008, 4:45pm)

Title: Coin weghting: 13 coins with 2 defected coins
Post by wonderful on Apr 3^rd, 2008, 4:45pm

I posted the same question in the "easy" section a a follow-up to Hippo's correct answer for the case of 8 coins. That said, it might be more relevant to post this question here:

There are 13 coins of which 11 weighs A g each. The other two are defected. One weighs (A+ 2) g and the other weighs (A-2) g.

Can you find out the two different coins using minimum weightings?

Have A Great Day!

Title: Re: Coin weghting: 13 coins with 2 defected
Post by Grimbal on Apr 4^th, 2008, 6:00am

Are these weightings on a 2-pan scale or on a scale that gives the weight?

Title: Re: Coin weghting: 13 coins with 2 defected
Post by Hippo on Apr 4^th, 2008, 1:11pm

I expect its the same puzzle with 8 replaced by 13, so the 2pan scales are expected.

So for the start there is 3⁴<13*12<3⁵ initial positions so we are trying to find solution on 5 measurements.

Title: Re: Coin weghting: 13 coins with 2 defected coins
Post by wonderful on Apr 4^th, 2008, 9:14pm

[hide]5 is the correct answer.[/hide] Next, we would like to design a weighting scheme to achieve this target. Result from the 8 coins can be used here.

Have A Great Day!

Title: Re: Coin weghting: 13 coins with 2 defected coins
Post by wonderful on Apr 14^th, 2008, 2:31am

It has been a while and it seems that nobody has come up with a solution. As such, I would like to give some hints here:

[hide]In the first three weighting we can do something like this:

(5, 6, 7, 8) ? (9,10,11,12)
(2, 8, 11, 12) ? (3, 4, 9, 10)
(1, 4, 6, 10) ? (3, 7, 9, 12)[/hide]

After that, there are two more weightings.
Let's continue.

Have A Great Day!