6. The set contained weights of 43, 70, and 57 grams, with an equal number of each type. Maly lost several weights (less than half), weighed the remaining on the scales, and got 20172 grams. How many and which weights were lost?
Solution (1). If the weights had not been lost, the total weight would end in 0. Therefore, the weight of the lost weights ends in 8. This can only be the case if 4 weights of 57 g are lost (losing 70 g or the pair $43+57$ does not affect the last digit of the total weight).

Solution (2). Let's divide the initial set of weights into triples $43+70+57$. In each triple, the total weight is 170 g. Note that no more than $4 \cdot 70=280$ g has been lost. Therefore, we need to find all numbers from 20172 to 20452 that are multiples of 170. There are only two such numbers: 20230 and 20400 g.

In the first case, 58 g have been lost, which is impossible. In the second case, 228 g have been lost. This is only possible if 4 weights of 57 g have been lost. Indeed, the number of lost 70-gram weights must be even (otherwise, the lost weight would be odd). If no 70-gram weights have been lost, the maximum possible lost weight is $4 \cdot 57=228$ g. If two 70-gram weights have been lost, 88 g remain for the two remaining weights, which is clearly impossible to achieve.