Problem of the Week #3: Monday Jan. 23rd, 2023 As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems. Please register for an account if you would like to join the discussion below or share your own problems. Please refrain from posting full solutions.
a). How many ways are there to make exactly 1 dollar using all the Canadian coins currently in use? (not including pennies)
b). How many ways are there to make exactly $100 using all the Canadian coins and bills currently in use? (not including pennies)
c). If you list all the amount of money that can be made using all the Canadian coins and bills currently in use from 0 to $13.50, in increments of 5 cents, which amount has the biggest difference in the number of ways to make it compared to the previous increment? For example, there are 8 ways to make 45 cents and 10 ways to make 50 cents. Therefore the amount of 50 cents has a difference of 2 ways to make it compared to its previous increment.
d). How many amounts have this exact difference in c) compared to its previous increment between 0 and $50?
e). When are the first and the last time we see this exact difference on the list of amounts if we continue the list indefinitely?
f). Share your own problem(s) inspired by this problem.