So a riddle today.
I have 13 coins. They like many other things have weights. These weights happen to be positive numbers (we're going for realism here). They also have the property that if I remove any one coin I can split the remaining 12 into two groups of 6 which have the same total weight. Does this guarantee that all the coins have the same weight?
Part a. If the weights are integers.
Part b. If the weights are allowed to be any positive real.
Part c. Sod positivity and indeed reality. Let's let the weight of the coins be any complex number. .
Have fun. Solution to come soon.