202. Nuts for Monkeys. One person brought a bag of nuts to the monkey enclosures. It turned out that if he divided these nuts equally among 11 monkeys in the first cage, there would be one extra nut; if he divided them among 13 monkeys in the second cage, there would be 8 nuts left; and finally, if he divided them among 17 monkeys in the last cage, there would be 3 nuts left.

It also turned out that if he divided the nuts equally among 41 monkeys in all three cages or among monkeys in any two cages, in any of these cases there would be leftover nuts.

What is the smallest number of nuts that could have been in the bag?
202. The smallest number of nuts is 2179. It is best to deal only with the first two cases at first and find out that 34 (or 34 plus any multiple of 143) satisfies the condition for 11 and 13 monkeys. Then, the smallest number of this kind that satisfies the condition for 17 monkeys should be found.