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Mon 24 Oct, 2011 04:28 pm
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?
@Lindastanich,
Working backwards:
(5+3)*2 = 16
(16+2)*2 = 36
(36+1)*2 = 74
Billy started with 74 pieces.
@Lindastanich,
A little more tedious than Markr
n=total # of pieces
A=amount taken by Freddy
B=amount taken by Sharkie
C=amount taken by Ninjie
A+B+C+5=n
A=n/2+1=(n+2)/2
B=(n-A)/2+2=(2n-(n+2)+8)/4=(n+6)/4
C=(n-(A+B))/2+3
A+B=(n+2)/2+(n+4)/4=(3n+10)/4
C=(n-(3n+10)/4)/2+3=(n+14)/8
A+B+C+5=(3n+10)/4+(n+14)/8+5=(7n+74)/8=n
8n=7n+74
n=74
Check
A=(74+2)/2=76/2=38
B=(74+6)/4=80/4=20
C=(74+14)=88/8=11
36+20+11+5=74
OK
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