FYSE 1176: Discovering Infinity                                                                                        Fall 2006

Four Solutions of the Hershey Bar Problem

Solution 1

Let X represent the number of bars A of chocolate you can purchase for $1. Then X = 1 + A where A is the number of bars of chocolate 1 coupon is worth. Now A is one-tenth of X.  Thus X = 1 + X/10.  Solving this equation for X yields X = 10/9. Once we know $1 buys 10/9 bars, we see that (9/10)$1 buys (9/10)(10/9) = 1 bar. Hence 90 cents buys one bar of chocolate.

Solution 2

$1 gets you a bar and a coupon. Now 10 coupons also gets you a bar plus a coupon so 1 coupon is worth 1/10 bar plus 1/10 coupon and that 1/10 coupon is worth (1/10) of 1/10 of a bar and (1/10) of (1/10) of a coupon and so on. Thus the number of chocolate bars purchasable by $1 is given by        

        

so

Subtracting the second equation from the first gives so X = 10/9.  As was the case with Solution 1, once we know X = 10/9, we can conclude that the price for the chocolate is 90 cents per bar.

Solution 3

Since each can be traded in for the same quantity Ð a package containing one chocolate bar and one coupon Ðit must be the case that a $1 bill and 10 coupons have equal value. Hence 1 coupon is worth 10 cents. Thus a dime of each $1 purchase must be paying for the coupon; the remaining 90 cents pays for the chocolate.

Solution 4

Walk in to the candy store, grab 10 wrapped bars and then open them up and extract the 10 coupons. Go to the clerk and hand over $9 and the coupons. You will then have exactly 10 bars of chocolate (and 0 coupons) and you will have $9. Thus you got each of the candy bars for 90 cents.