Question

Dear Mitch,

With the anniversary of the birthday of Magician-and-Legendary-Escape-Artist Harry Houdini coming up in a week, it would be great if you could post another question that would be as interesting as the one you had the other day for middle school math students.

Thank you,

Ms. M.

Atlanta, GA

Answer

Dear Ms. M,

Sure!

Legend has it that the great magician you mention, Harry Houdini, performed a trick that enabled him to turn pennies into nickels, turn nickels into dimes, and turn dimes into quarters. (However, as is often the case with magic tricks, each time he performed one of these little feats, he needed to use a few secret supplies (such as a small bit of wax, a loop of special copper thread, and a new toothpick). As a result, each 'transformation' from one coin to another had a small cost associated with its performance.

Mr. Houdini's costs were as follows:

TRANSFORMATION COST

To change a penny into a nickel 2 cents

To change a nickel into a dime 3 cents

To change a dime into a quarter 4 cents

(The transformations could only be done one of the above steps at a time. So, for example, to change a penny into a quarter would cost Mr. Houdini a total of nine cents, because first the penny would have to be changed into a nickel, which cost him 2 cents, then that nickel would have to be changed into a dime, which cost him 3 cents, and then that dime would have to be changed into the final quarter, costing him 4 cents. So, to complete the stunt it would cost 2 cents + 3 cents + 4 cents = 9 cents)

Using a combination of these three tricks, how much "profit" would the trick appear to produce, if he began with a pile of change that was comprised of 3 quarters, five dimes, ten nickels, and six pennies.... AND WAS ASKED TO TURN THE PILE INTO $1.50 in quarters, and the rest of the change into dimes?

This is trickier than it might first appear, because you have to figure out how much the change was worth that he began with, the amount the collection of change was worth at the end, and (somehow) figure in the costs from all the changes necessary. Try to maximize the "profit", by not doing any unnecessary transformations, and, well, Good luck!

Hope this provides the fun and exercise you were hoping for.

I will answer it before the anniversary of the birthday of the legendary magician, which is Monday, March 24th!

Magically,

Mitch