Three Beggars - Solution

by
Erik Oosterwal



The solution to this problem requires you to work backwards from the end until you get to the beginning.

At the end of her journey, the lady had 1 penny left.  We're told she gave 3 cents more than half of her purse to the third beggar, so we add 3 cents to her one cent, double that amount to come up with a total of 8 cents in her purse before  her visit with the third beggar.

She gave 2 cents more than half her purse to the second beggar.  If we add those 2 cents to the eight she had before seeing the third beggar and double that amount, we get a sum of 20 cents in her purse before her visit with the second beggar.

She gave 1 cent more than half her purse to the first beggar.  If we add that one cent to the 20 she had before seeing the second beggar and double that amount we find she started her journey with 42 cents.

To verify this answer let's work through the problem again with the starting point of 42 cents.  One half of 42, plus one cent is 22 cents.  The first beggar received 22 cents and the lady was left with 20.  The second beggar received one half her purse plus 2 cents or 12 cents.  The lady was left with 8 cents.  The third beggar received one half of her purse plus three cents or 7 cents, and the lady was left with only a penny.


All original puzzles and solutions are © Erik Oosterwal 1993-2008

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