8.3. There are 10 weights, and it is known that if any one of them is removed, the remaining 9 weights can be divided into three groups of equal weight. Must all 10 weights necessarily be of the same weight?
Answer: Not necessarily.

Solution. Here is an example: suppose there are seven weights of 1 g and three weights of 7 g. Then, if we remove a 1 g weight, we can arrange them as follows: $1+1+7=1+1+7=1+1+7$, and if we remove a 7 g weight, then $1+1+1+1+1+1+1=7=7$.