7.3. A flock of geese was flying over the lakes. On each lake, half of the geese and another half-goose landed, while the rest continued flying. All the geese landed on seven lakes. How many geese were in the flock?
7.3. Answer: 127. Let's mentally add a bird, for example, a duck, that flies with the flock all the way to the last lake. Then, at each lake, exactly half of the birds land, and on the seventh lake, two birds land - the goose and the duck. This means there were $2^{7}$ birds in the flock, of which $2^{7}-1=127$ were geese.