How would you like to run a roller coaster right through your home? It could start at any high spot, run through bedrooms and the kitchen, and pop out the front door. Someone actually built a coaster like this as a way to sell a house. Dutch realtor Huizen Promoter built a coaster through one home they were trying to sell, as a way to excite people who might buy it. The coaster started with a steep drop into the garage, then used that speed to run up the stairs into the kitchen and then roll through other rooms. It even rolled back outside onto the deck for a spin, before zooming back inside. The builders, who had never built a coaster before, had to figure out all the numbers: how wide can the track be? How much weight can it hold without crashing down? They managed to get it right. The question is, will the new owner keep the coaster in place?
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
