The famous 12 counterfit coin problem can be solved using 3 weighings. If youre not familiar with this problem its on the site.
Also if you want to solve for 13 weights you must have one that is known to be of the correct weight.I was told the problem incorrectly by my logic teacher:
13 weights all unknown
I thought that he was mistaken so I decided i should prove if its possible, which i did.
There are 3 weighings and each can have 3 possibilit's. More, less or equal. Therefore the total number of outcomes is 3x3x3=27
There are 13 possible counterfit weights either weighing more or less. 13x2=26
There are 26 possible answers and 27 different possible outcomes therefore it can be proven.
If anyone can help explain this please do. its take up some of my recent life...
thanks