Marc, himself, his blogs, and you reading them.
July 21, 2004
Just finished reading (dutch version of) Fermat's Last Theorem by Simon Singh. I just found this website covering the same topic, but still need to heavily recommend the book: it reads actually as a whodunnit and succeeds very well at transferring a sense of 'passion' for the numbers. The story also involves prizes to be won, an almost suicide and a duel at dawn.
Apparently this book seems to be a textual rundown of a BBC Horizon series. For which I only found this 404 (linked from here). Would be nice to ever get to see the VHS copy of this.
In any case, the book also had this nice little riddle said to be originated by Bachet (who was the author of the translation with the way too small margins...):
What is the least amount of (and which are the) reference weights that you need to be able to weigh any discrete kilogram between 1 and 40 kg on a balance with two scales?# Posted by mpo at 05:37 PM | TrackBack
I didn't check your answer but can tell you that most people arriving at 6 mostly just take the powers of 2: 1,2,4,8,16,32
Bachet however found a solution that only takes 4.
He really used the fact that it is a balance with TWO scales.
Posted by: -marc= at July 26, 2004 09:34 PM
I guess the anwer to the riddle is 6, with the reference weights being 1, 2, 4, 5, 10 and 20 kg? Maybe I am wrong but any discrete kilogram between 1 and 40 can be weighted with these weights on a balance with 2 scales.
Did I miss any mathematical magic by just calculating the possible combinations out of my head?
Posted by: Wim at July 26, 2004 05:51 PM