The vexatious vault value veracity validation problem
This problem was originally posted by Karl Sharman (with a less idiotic title).
Whilst I was away under the pretence of work, a nearby bank uncovered a plot to swap the gold in their vaults with counterfeits. It was determined that all the gold bars in three of the Bank’s seven vaults were replaced with counterfeits. The other four vaults were uncompromised. The plot was foiled through the poor math skills of the thieves: while the real gold bars weigh ten kilograms, the counterfeits all weighed nine kilograms.
I was asked to work out which was the real gold, and which was the fake. I, being really bad at maths, so Chris tells me decided to recruit your help.
Your mission, should you wish to accept it, is determining which vaults have real gold, and which are just gold-plated bars of platinum.
The Bank Director has made the following generous offer: If you can determine the counterfeits using just one weighing on a scale, you can keep one bar as a souvenir.
Here are the rules:
This is a scale, not a balance, but you can weigh as many bars together as you like.
Only one weighing!
The bars will be handled by professional guards, so you won’t have a chance to “feel” their weights.
Each vault contains several hundred bars.
The guards have requested that you try to keep the number of bars you need to a minimum.
How do you do it, and what is the minimum number of bars…?