perplexus.info :: Just Math : Money Division Muse

Money Division Muse (Posted on 2014-05-27)

Mr. Saunders has recently passed away.

In his will, he has divided his money among his 7 children, 7 stepchildren and a manager.

Mr. Sanders’ will stipulated:

First give $1 to manager, and 1/7th of the remaining to the eldest child.
Now give $1 to the manager and 1/7th of the remaining to second oldest child and so on.....
After giving the money to the seventh (youngest) child, divide the remaining money among the seven stepchildren equally.

Knowing that:

The ages of each of the seven children are different, and:
Each of the 15 individuals received a positive integer number of dollars

What is the minimum amount of money that Mr. Saunders had left behind?

Extra Challenge: A non computer program aided solution.

Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Solution: (Hide)

823537 is the minimum amount of money that Mr.Saunders had left behind,
Details given, from eldest-child distribution to seventh-eldest child, showing manager's cut, child's cut and what's left after each distribution:
mgr child what's left 1 117648 705888 1 100841 605046 1 86435 518610 1 74087 444522 1 63503 381018 1 54431 326586 1 46655 279930
that last remainder being divided into seven amounts of 39990 each
For an explanation, refer to the analytic solution submitted by broll in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(2): So close yet so far?	broll	2014-05-28 09:12:04
re: So close yet so far?	Charlie	2014-05-27 23:36:45
So close yet so far?	tomarken	2014-05-27 17:03:58
computer solution	Charlie	2014-05-27 15:57:58

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