When Buratino went to the VMSh classes, Papa Carlo promised to pay him one kopeck for the first correctly solved problem, two kopecks for the second, four kopecks for the third, and so on. In a month, Buratino received 655 rubles 35 kopecks. How many problems did he solve?

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For simplicity in calculations, let's assume that before attending the VMSh classes, Buratino had one kopeck. Then, after solving the first problem, Buratino will have 2 kopecks. Solving the second problem, he will receive two more, and he will have $2 * 2=4$ kopecks. Solving the third problem, he will receive four more and will have 8 kopecks. We see that after solving each subsequent problem, Buratino's wealth doubles. Continuing the calculations, we get that after solving 16 problems, Buratino will have $2^{16}=65536$ kopecks. This amount matches Buratino's wealth after a month of classes, so he must have solved exactly 16 problems.

## Answer

16 problems.