How would you like to build a roller coaster right through your home? One company actually did this to sell a house! Huizen Promoter’s coaster started with a steep drop into the garage, then used that speed to run up the stairs into the kitchen and through other rooms. The builders had to figure out all the math: how wide can the track be? How much weight can it hold? And our question is, did the new owner ride it?

*Wee ones:* How many rooms do you have in your home? See how many you can count!

*Little kids:* If your coaster zooms down sets of stairs 3 times and goes back up 2 times, how many slopes does it ride in total? *Bonus:* If you want the coaster to start indoors, zip outside and back inside a few times, and end outside, will it pass through windows an even or odd number of times?

*Big kids:* If your coaster runs 10 feet through your bedroom and you have 36 feet of track in total, how much track do you have for outside your room? *Bonus:* If you build 2 straight runs and you have 14 sections of track, how many different ways can you divide the track sections between the two? (Assume at least 1 section for each.)

*The sky’s the limit:* If you’re building 3 straight runs and have 7 sections, how many ways can you divide *those* among the 3 runs?

Answers:

*Wee ones:* Different for everyone…count them in your head, or walk around to count!

*Little kids:* 5 slopes. *Bonus:* An odd number, since going outside will take 1 pass, or 3, or 5…

*Big kids:* 26 feet. *Bonus:* 13 ways: 1 and 13, 2 and 12, 3 and 11, and so on up to 13 and 1.

*The sky’s the limit:* There are 15 ways to divide them. The first stretch can have anywhere from 1 to 5 sections, but there are more combinations when the first stretch uses just 1 section than when it has 5. You end up with 5+4+3+2+1 combinations, as follows:

1,1,5, 1,2,4, 1,3,3, 1,4,2 and 1,5,1

2,1,4, 2,2,3 2,3,2, and 2,4,1

3,1,3, 3,2,2 and 3,3,1

4,1,2 and 4,2,1

5,1,1