How many ways can you change a dollar?
The old challenge was by Joe Shipman.There are over 300 ways to make change for a dollar, according to Larry King.Is this correct?Assume only current denominations.
Answer.You can count a one-dollar coin in change.Raymond Hettinger appended all the possibilities to the end of the column.There are 292 possibilities other than a one-dollar coin.
There are 50 combinations, given that 1 half dollar will be used.0 quarters with 5 dimes or less.
There are more than 200 combinations with no half dollars used.There are 2 quarters with 5 dimes.10 dimes (1), 9 (3), 8 (5), 7 (7), 6 (9), 5 (11), 4 (13), 315) were used in the first quarter.
With generating functions, computations can be accomplished.Herbert's "Lectures on Integer Partitions" can be found at http://www.math.upenn.edu/wilf.
The following table shows the number of ways in which you can exchange different units of currency.
I allowed $2 bills.I couldn't tell the difference between $1 coins and $1 bills.I decided that I should distinguish among the 50 different quarters now being issued.I didn't want to do that.
According to Walter Wright, a dollar coin can't be considered change for a bill because it's a number of coins or bills whose total value equals a single larger coin or bill.
There is questionable mathematics.Three years ago, Al went to the Citibank ATM in Midtown Manhattan to withdraw cash.The machine rejected my request.
There is a new challenge.What is the largest positive number that you can represent with three mathematical symbols?The smallest?
To be eligible for Flatland and other book awards, send answers, comments, and new questions to Frank.Morgan@williams.edu.The next math chat will have winning answers.On the first and third Thursdays of each month, there is a math chat.Prof. Morgan's website can be found at www.williams.edu/Mathematics/fmorgan.
There is a list of past challenge winners and a $1000 Math Chat Book QUEST available from the MAA.
1 : 1 dollar, 0 half-dollars, 2 quarters, 1 dime, and 2 nickels.