Chapter 10.4, Problem 21MS

Coin coupling. For this challenge, you will need five pennies, five nickels, and five dimes. The goal is to fill each cell of the following “bank” with a pair of two different coins paired in all six ways the coins can be coupled, that is, penny-over-nickel, nickel-over-penny, penny-over-dime, dime-over-penny, nickel-over-dime, and dime-over-nickel.

The rules: You start with the penny-over-nickel pair already shown in the bank. You also start with a “Moveable Coins” column and a penny, a nickel, and a dime ready to arrange in it, but don’t put them in yet. To get another pair of coins into the bank, look at a pair of coins you already have in the bank. Arrange the three coins in the Moveable Coins column by starting with the ordering of the pair from your bank and then putting the third coin above or below the pair. (Don’t take the coins from your bank. Once a pair is in the bank, it stays there. Just arrange the corresponding moveable coins appropriately.) Since penny-over-nickel is in your bank, you could create the column as shown, penny-over-nickel-over-dime (or, alternately you could create dime-over-penny-over-nickel for example), in the Moveable Coins column:

Now you are allowed to put the top-over-bottom pair that is in your moveable column, in this case, penny-over-dime, in another cell in your bank. Your challenge: Can you get all six possible pairs in your bank?