I was given this riddle that has been bothering my mind for past few hours.
Given the following information:
the weight of coin types:
- 1p - 1.62g
- 2p - 2.11g
- 5p - 2.57g
- 10p - 2.49g
- 20p - 3.21g
- 50p - 3.91g
- 100p - 5g
- 200p - 5.11g
- 500p - 6.51g
Is it possible to develop an algorithm that would allow you to estimate worth of these coins without sorting them or weighting in portions?
If yes, then for up to how many coins? If no, why?
I've come to conclusion that yes, you can but only up to 2 coins - did anyone else arrive to such conclusion?
Assuming the coin weights are within $0.005 g$ and you can weigh within that, yes I believe you can weigh any pair of coins and know the value. You would have to produce a table of all the possible weights and show there were no duplicates.
To show you cannot do it for three coins just show that $1p+100p+100p$ weighs $1.62+5+5=11.62$ and $200p+500p$ weighs $5.11+6.51=11.62$ I didn't find a case where two groups of three coins matched in weight so if you know you have three coins you can still do it.