Mr. Gooch loves to bring home sweet things for his four 
sons.  Today he brought a box of chocolates.  His eldest 
son, Ricky, ate half the chocolates plus half a chocolate. 
The next, Jeremy, ate half of what was left, plus half a 
chocolate.  His third son, Gregory, ate half of what was 
left plus half a chocolate.  And Lincoln, the youngest, 
ate the last two chocolates in the box.  How many 
chocolates were there in the box? 

Note: none of the chocolates was cut in half.
 
 
 
 

                 THE SOLUTION

Its best to count backwards, working up to the oldest Gooch.
If Lincoln took two chocolates, and that represented half of
what Gregory had left him less half a chocolate, there had
to be 5 candies-when Gregory was ready to take his turn:
{2+½}X2=5  If Jeremy left five chocolates, then he had to
have the choice of 11: {5+½}x2=11  And Ricky, in order to
leave 11, would have had to start with 23 chocolates:
{11+½}X2+23  Therefore, the total number of chocolates in
the box was 23, and they divided up quite unfairly: 12, 6,
3, and 2.
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