# Livin’ in a Schoolbus

Here's your nightly math! Just 5 quick minutes of number fun for kids and parents at home. Read a cool fun fact, followed by math riddles at different levels so everyone can jump in. Your kids will love you for it.

# Livin’ in a Schoolbus

September 2, 2014

As the school year winds up, a lot of kids get to ride the bus to school, which can give your day a fun start. But how about riding that bus home and staying in it because it’s actually your home? An architect named Hank Butitta decided to try out this idea. He bought a used schoolbus, pulled out all the seats, built in sinks, beds and whatever else a home needs, and lined the ceiling and walls with light wood to make it nice and homey. The bus has great indoor light thanks to the dozens of windows, and the even 28-inch spacing of the windows and seats gave him a helpful grid to line up the new furniture. We’re now wondering if Hank wants to try this with an airplane…in the meantime, if you love your bus ride to school, here’s a way to enjoy it around the clock.

Wee ones: If that bus has 2 front wheels and 2 back wheels like most schoolbuses, how many wheels does it have?

Little kids: Hank spent \$3,000 buying the old bus and \$6,000 fixing it up. How much did he spend in total on his new home?  Bonus: If you normally ride the bus 1 hour per day total, how much more time could you spend there in 1 day if you stayed the whole time? (Reminder: A day has 24 hours.)

Big kids: If Hank’s bed is 84 inches long, and each 28-inch deep seat seated 2 kids, how many kids could have sat where the bed is now?  Bonus: If the bus had 20 rows of seats that are each 28 inches front to back, how long a house did that bus give him once he emptied it? (Hint if needed: You can break this into pieces by multiplying by 10 and then by 2, or in the other order.)

The sky’s the limit: Suppose the bus had a lucky 13 rows from front to back. If Hank wanted to build in an 84-inch bed, an 84-inch desk space, a 140-inch kitchen, a 140-inch tropical aquarium, a 56-inch wide toilet, a 112-inch couch for guests, and a 112-inch-wide marble ramp, how many different ways could he line these up to fit? (Note: you might want paper and pencil to tally up the combos!)

Answers:
Wee ones: 4 wheels.

Little kids: \$9,000.  Bonus: 23 more hours.

Big kids: 6 kids, since the bed takes up 3 rows.  Bonus: 560 inches.

The sky’s the limit: There are 1,152 arrangements. First, figure out how many seat rows each item takes up: 3 each for the bed and desk, 5 each for the kitchen and aquarium, 2 for the toilet, and 4 each for the couch and marble ramp. You’re now finding all the ways to fit 3, 3, 5, 5, 2, 4, and 4, given that together they add up to 26 spaces, which is exactly the total space given. So the first few items have to add up to exactly 13, leaving 13 for the rest as well.
– There are only 4 possible number groupings within which you can rotate: 5+5+3, 4+4+2+3, 5+4+4, and 2+3+3+5.
– Each set can swap in different items for the lengths. So 5+5+3 can have K, A and B (kitchen, aquarium and bed) or K, A, D (kitchen, aquarium and desk). Similarly 4+4+2+3 has 2 choices for the 3 (B or D), giving us 2 combos. 5+4+4 has 2 choices for the 5, as does 2+3+3+5.
– Once you pick which way one set goes, its matching set takes whatever is left: each 5+5+3 goes with a 4+4+2+3, and each 5+4+4 goes with a 2+3+3+5.  So there are still just 2 ways to do each of the 4 sets (8 total), and you can put any of the 8 on the left side and its match on the right.
– For each of those 8 choices, the side with 3 items has 6 possible line-ups
– For each of those 6 line-ups, the other side with 4 items has 24 possible line-ups

So by our count, Hank has 8 x 6 x 24 options, or 1,152 ways to arrange the furniture!

### Laura Overdeck

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.