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Okay, here's one with a story :) Let's see if this is entertaining enough :D

Here is a problem that involves being jerk.

You receive a parking ticket and decide to pay in the least
convient way possible... change. This decision comes to mind
because the tickets are in strange amounts because they use
the cents portion for some kind of internal encoding.

You decide to pay all in pennies but when you start to collect
them someone informs you that although change will be accepted,
if the counts of coins exceed the quantities required for a wrapper
then you must roll them.

US Coinage count to a roll
0.01 = 50
0.05 = 40
0.10 = 50
0.25 = 40
0.50 = 20
$1.00 = 25 (small) or 20 (large)

Question 1.
How many rolls and free coins of each can you provide to pay your
$100.37 ticket in order to use the highest count of unrolled coins?

Considering that a ticket can cost anywhere from $1.00 to $250.00.
You start telling everyone else about your plan and they decide to
play too, so you calculate how they should pay as well.

For example, 45 pennies 21 nickles for a $1.00 ticket might be
pretty obnoxious :).

Question 2. Which fine amount (in that range) would allow you to
provide the highest number of unrolled coins?

Question 3. The parking authority figures out what you are doing
and decides to change things up by hiring you. Your job is to
determine the best fine values to get paid in the least amount of
unrolled coins. What are those amounts what are those amounts (still
within that range of $1.00 to $250.00)

Just to clean it up a little, and add some more entertainment.

Okay, here's one with a story :) Let's see if this is entertaining enough :D

Here is a problem that involves being jerk.

You receive a parking ticket and decide to pay in the least
convient way possible... change. This decision comes to mind
because the tickets are in strange amounts because they use
the cents portion for some kind of internal encoding.

You decide to pay all in pennies but when you start to collect
them someone informs you that although change will be accepted,
if the counts of coins exceed the quantities required for a wrapper
then you must roll them. You also figure out that collecting all
these coins is a bit of a nuisance for you. So your goal is to
reduce the overall number of coin rolls while maximizing the
number of free (or unrolled individual coins).

US Coinage count to a roll
0.01 = 50
0.05 = 40
0.10 = 50
0.25 = 40
0.50 = 20
$1.00 = 25 (small) or 20 (large)

Question 1.
How many rolls and free coins of each can you provide to pay your
$100.37 ticket in order to use the highest count of unrolled coins
while using the least number of rolled coins?

Considering that a ticket can cost anywhere from $1.00 to $250.00.
You start telling everyone else about your plan and they decide to
play too, so you calculate how they should pay as well.

To make things a little more interesting, you show up at a city council
meeting and propose that because of the time involved in processing
unrolled coinage that the parking authority should, rather than
bother with unrolled coins, all unrolled coins they collect should
just be donated to the city coucil's general fund. They pass this
unanimously.

For example, 45 pennies 21 nickles for a $1.00 ticket might be
pretty obnoxious :).

Question 2. Which fine amount (in that range) would allow you to
provide the highest number of unrolled coins?

Question 3. The parking authority figures out what you are doing
and decides to change things up by hiring you. Your job is to
determine the best fine values to get paid in the least amount of
unrolled coins. What are those amounts what are those amounts (still
within that range of $1.00 to $250.00)

@Absinthe can you clarify the situation with dollars? It's unclear whether (a) the US has large- and small-sized dollars, or (b) there is a single size of dollar that can be put into a large- or small-sized wrapper.

@khird Yes we still have the Ike's (Eisenhower 38.1 mm dollars) Huge wonderful pieces of clad coinage. :) But we also have Susan B. Anthony "Carter Quarters", Sacagawea "Golden Dollars" and Newer native american and presidential head dollars, all in the 26 mm variation. All of them are much less interesting than the Ike, but they work for change in stamp machines at the post office. Most Americans, don't like dollar coins. But I digress.

The 38mm ones are 20 to a roll and the 26mm ones are 25 to a roll, and can't be mixed together in a roll.

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