[ Rule of product]

There are four weights and a two-pan balance without a pointer. How many different weights can be accurately weighed with these weights if

a) the weights can only be placed on one pan of the balance;

b) the weights can be placed on both pans of the balance

#
б) We can distribute the weights into 3 piles in $3^{4}=81$ ways (see problem $\underline{60348}$). We will set aside the first pile, and place the other two on the scales (the case where both of these piles are empty should be discarded). Since it does not matter which pans these piles end up on, 80 should be divided in half.

## Answer

a) $2^{4}-1=15$;
б) 40 weights.