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Pearls and Girls

Math brain teasers require computations to solve.

 

Puzzle ID:#13063
Fun:*** (2.7)
Difficulty:*** (2.74)
Category:Math
Submitted By:willymapo*cr****
Corrected By:Sunrose

 

 

 



Once an old man died, and in his Will he stated that all the pearls he kept in a little bag were to be distributed among his daughters. To make things fair, the distribution must be done in the following way:

The older girl should receive one pearl, and a seventh of the remaining pearls in the bag.

The second girl should receive two pearls, and a seventh of the remaining pearls in the bag.

The third girl should receive three pearls, and a seventh of the remaining pearls in the bag.

And so on until all the pearls are exhausted.
Needless to say, the younger girl grew angry, and went to talk to the Judge because, if distributed that way, she probably would not get a pearl at all.
The wise Judge looked at her and said: "Don't worry, my child. Your father was a wise man. He made everything quite right so that, after all the pearls are given, each one of you will have the same quantity of pearls and there will be no pearls left."

And so it was.
How many pearls were there in the bag?
How many daughters did the old man have?
How many pearls did each girl get?

Open Calculator

Hint

If there are no pearls left, how many pearls are in the bag for the last girl? How many pearls did the second-to-last girl get?
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