The Truth about Toilet Paper

by Laura Overdeck

Toilet paper is something we don’t think about much, except when it runs out. Then it’s an emergency! But toilet paper is a very cool math object. How long is a whole roll of it? How many times does the paper wrap around? How do they even make toilet paper? Most toilet paper comes from recycled paper. Regular old paper is thrown into water and mushed into a pulp, to wash out ink and dirt. Then rollers smush the pulp into a really thin sheet. Once it dries, the soft paper is rolled onto tubes that are more than 5 feet long, probably longer than you! At the end, they chop that into little rolls, because no one’s butt is that wide. Now let’s see how those squares add up.

Wee ones: Pull on a roll of toilet paper until 5 squares have rolled off.

Little kids: If you have a pack of 6 toilet paper rolls, and you and your friend roll 2 of them down the hall in a race, how many rolls do you have left?  Bonus: People go to the bathroom about 6 times a day. If you use 3 squares each time, how many squares do you use in 1 day? Count up 6 at a time!

Big kids: If you pull the toilet paper really hard to make it all fly off, and you whip off 40 squares on the 1st pull and 1/2 as many on the 2nd pull, how many squares total do you spin off?  Bonus: If a roll has 240 squares, each 4 inches long, how long is the whole roll in feet? (Hint: 4 inches is a nice neat fraction of 12 inches…)

The sky’s the limit: If you spin out 20 layers of paper, and the 1st 4 layers have 8 squares each, the next 4 layers have 7 squares each, then 6 squares each, 5 squares each, and finally the last 4 layers have 4 squares each…can you find the shortcut to figure out how many squares you pulled off?

Wee ones: Count the squares: 1, 2, 3, 4, 5.

Little kids: 4 rolls.  Bonus: 18 squares.

Big kids: 60 squares (40+20).  Bonus: 80 feet! (or 960 inches).

The sky’s the limit: 120 squares. If you don’t feel like adding up all those little numbers, you can see that having 8 squares on a layer and having 4 on another is the same as each layer having 6 squares.  Same for 5 squares vs. 7 squares on the same number of layers: it’s the same as having 6 on all of them.  So they average out to 6 squares per layer for 20 layers.

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