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        riddles >> hard >> scales
        
(Message started by: Chekov on Mar 6^th, 2007, 9:57am)

Title: scales
Post by Chekov on Mar 6^th, 2007, 9:57am

I dont know if its been done here yet so Ill just put it in. lets c.

You got 12 balls. doesnt matter the size. these 12 all got the same weight. except for 1. you got a scale/balance. The ones they had in the medieval time.

you may use the scales 3 times. then I want to know:
- which ball is it that is different
- is it weighing more or less then the normal ones

regards,
Chekov

Title: Re: scales
Post by jollytall on Mar 6^th, 2007, 11:51am

It is somewhere on the forum (in the easy section).

Just a thought for someone who still wants to solve, rather than search:

[hide]There are 24 possible outcomes, and the three measuerement can have 3 outcomes 3 times, a total of 27 cases. So it is not necessarily impossible (actually possible), but don't loose too many cases.[/hide]

Title: Re: scales
Post by Aryabhatta on Mar 6^th, 2007, 11:54am

Probably discussed earlier too..

What if you are only allowed to refer to the results of weighings after you are done with all your weighings.

i.e you cannot use the outcome of the first weighing to determine what you will do for the second weighing etc.

Title: Re: scales
Post by jollytall on Mar 6^th, 2007, 12:07pm

I was wrong: it is in the hard section, since in the original Wu list of riddles it was considered "Relatively Hard":
http://www.ocf.berkeley.edu/~wwu/riddles/hard.shtml

(look for 12 Balls).

The thread that discussed it is here:
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1027806808

I also found a subsequent one discussing it even further:
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1132320902;start=0#0

Re the subsequent question of Aryabhatta:
I am having doubts whether it is possible. Again, as I said earlier you can loose (get redundant results) only 3 times. I am almost sure, without using the earlier results you necessarily loose more.
I would look at the permutations of the three measurements to prove that there are more lost cases than 3.

Title: Re: scales
Post by Aryabhatta on Mar 11^th, 2007, 8:50am

on 03/06/07 at 12:07:32, jollytall wrote:

Re the subsequent question of Aryabhatta:
I am having doubts whether it is possible. Again, as I said earlier you can loose (get redundant results) only 3 times. I am almost sure, without using the earlier results you necessarily loose more.
I would look at the permutations of the three measurements to prove that there are more lost cases than 3.

I seem to recollect that it is always possible.