All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Train track shapes (Posted on 2011-08-01)
I have a toy train set with lots of curved pieces. If you put any 8 of these pieces together you can make a circle with radius r.

Ignoring the width of the track, find the area (in terms of r) enclosed by each of the following configurations:

1) As the train goes around the track clockwise it goes 5 turns right then 1 turn left. This pattern continues twice.

2) 6 right 2 left, twice.

3) 5 right 1 left 1 right 1 left, twice.

4) 3 right 1 left, four times.

5) 4 right 1 left 2 right 1 left, twice.

6) 5 right 1 left 2 right 1 left 5 right 2 left.

Bonus: Are there any other configurations using 16 or fewer of these pieces?

 Submitted by Jer No Rating Solution: (Hide) 1) (π+2√2)r2 2) (π+4)r2 3) (π+4√2)r2 4) (π+8+4√2)r2 5) (π+4+12√2)r2 6) Same as 1) Bonus: I don't think there are.

 Subject Author Date an answer to 1 thru 6 Dej Mar 2011-08-03 03:08:48 A start, with 1 and 2 (spoilers for these), and a thought Charlie 2011-08-01 14:00:06

 Search: Search body:
Forums (0)