There was a diamond broker who had 7 sons. Few months before his death he told his eldest son that he has hidden few diamonds somewhere and that when he dies he (the eldest son) should divide all the diamonds equally between 7 brothers. Few weeks later the father dies and the son gets the diamond and tells his younger brother that how they can have the diamonds equally between two of them with out telling others. When they divide the diamonds equally between themselves they are left with one diamond so they decide to include 3rd brother and divide the diamonds equally between them but again one diamonds is left. They bring the fourth brother but still one diamond is left so the fifth one comes in and then the sixth one but still one diamond is remaining. When they bring the seventh brother in the diamonds are equally divided.
The question is, how many diamonds are there, and how one diamond was left in
every division (each time diamonds were shared between 6 brothers until they
brought the seventh brother in). Diamonds are not allowed to be broken in two
pieces.
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Assuming that the number of diamonds are less than 500, then the number
of diamonds are 301. If the number of diamonds are more than 500, then the count
can be any of these 721, 1141, 1561, 1981, 2401, 2821, 3241, 3661, 4081, 4501,
4921, 5341, 5761, 6181, 6601, 7021, 7441, 7861, 8281, 8701, 9121, 9541, 9961,
...
