Let's loot!

Level pending

In a pirate band there are seven pirates, one of them is the "boss". Once they stole a bag of gold (coins). They formed a circle. One of the pirates (could be the boss) added the digits of the amount of gold coins, and he took as many gold coins as he got for the result. Then the pirate who stood on his right, did the same thing but only with the remaining gold coins. Following this procedure they recognized that when there were no gold coins left in the bag, each pirate had the same number of gold coins except for the boss, who took more than the others. If each pirate took gold coins the same numer of times and there couldn't be more than \(200\) gold coins in the bag, then how many possibe values are there for the numbers of gold coins in the bag (originally)?


This problem is from the "Kalmár László" Hungarian maths competition.
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