Here is my variation on a classic logic puzzle:
A butcher uses a balance scale in order to measure if he gives the right amount of meat to the customers.
For this scale he has six weights, all of which weigh a whole number of grams, for which he can weigh against the meat a maximum of all weights added together. If the scale is balanced he knows the meat weighs the same as the sum of all weights.
Furthermore, if he combines the weights in the right way he can weigh against meat weighing any whole number of grams under the sum of all weights and have the scale balance.
For example, if all the weights combined weighs 17 grams he can still use one or more weights to weigh 1 gram or 2 grams or 3 grams or 4 grams etc. all the way up to 17 grams, but not any more than 17 grams.
Knowing this, what is the most he could possibly weigh with these weights?
