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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