posted by Linda on .
Little Billy was out trick or treating on Halloween. He had gotten a lot of candy and was peering into his bag, when out from behind a tree came Freddy Krueger. Freddy reached into Billy's bag and took half of his candy plus one piece. Within a few steps, Billy encountered a Great White Shark, who reached into Billy's sack and took half of his remaining candy plus two pieces. Before Billy could turn and run, a Ninja Turtle, stole half of the candy that was left plus three pieces. Now Little Billy began to cry because he only had 5 pieces of candy left. How many pieces of candy did Billy have before Freddy, the Shark, and the Ninja Turtle raided his sack?
Let Billy have n pieces of candy. Tallying up all the thefts, we get
After Freddy, Billy has n - (n/2 + 1) = n/2 - 1
After Shark, Billy has n/2 - 1 - (n/2 - 1)/2 - 2 = n/4 - 5/2
After Turtle, Billy has n/4 - 5/2 - (n/4 - 5/2)/2 - 3 = n/8 - 17/4
n/8 - 17/4 = 5
n - 34 = 40
n = 74
Billy had 74 pieces
So, Freddy took 37+1 leaving 36
Shark took 18+2 leaving 16
Turtle took 8+3 leaving 5
working from the other end,
n = 2(2(2(5+3)+2)+1) = 74