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Pearls and Girls

Math brain teasers require computations to solve.

 

Puzzle ID:#13063
Fun:*** (2.69)
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?

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Comments

tissueAus*
Jun 17, 2003

Great job! That was a thoughy.
willymapo*cr*
Jun 26, 2003

Thanks!
In fact, the number of perls and girls can be calculated by a simple formula and create an complete set of teasers like this one.
javaguru*us*
Feb 26, 2009

It was a nice, although rather easy teaser. I basically did it the way described in your solution, but simpler. When the second-to-last daughter takes one seventh, there must be seven pearls left. The last daughter must then get the remaining six. The sixth daughter will take six pearls before taking one seventh, so there must be six daughters getting six pearls each and 6x6=36 pearls.

So that's simple enough, but why do there have to be seven pearls when the second-to-last daughter takes her pearls and not say 14? Because each daughter was taking one more pearl, the 1/7 that the second-to-last daughter takes must also be one pearl.

If each daughter took three pearls and then one seventh, the 1/7 the second to last daughter takes must be equal to three. (In this case there are six daughters getting 6x3=18 pearls each.)

geneHAG*
Jul 22, 2016

Talk about doing things the hard way!
(But I got it.)

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