6-4. In the store "Kopeechka", any item is sold for some number of rubles and 99 kopecks (possibly for 0 rubles and 99 kopecks). Different items may have different prices. Kolya made a purchase for 200 rub 83 kopecks. How many items could he have bought? Find all possible options.
Answer: 17 or 117.

Solution: We will buy items one by one. Then the number of kopecks will decrease by 1 each time, and after 0 kopecks comes 99 kopecks. The first time we get a whole number of rubles and 83 kopecks, by buying $100-83=17$ items. This option works: for example, 16 items could be bought for 0 rubles 99 kopecks each, and one more item for the remaining amount.

The second time we will get a whole number of rubles and 83 kopecks, by buying already 117 items. This option also works: for example, 116 items could be bought for 0 rubles 99 kopecks each, and one more item for the remaining amount.

The third time we will get a whole number of rubles and 83 kopecks, by buying already 217 or more items. This option does not work: for 217 items, we will spend at least 217 - 99 kopecks, which is clearly more than 201 rubles. Therefore, Kolya could have bought only 17 or 117 items.