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Train track shapes (Posted on 2011-08-01) Difficulty: 3 of 5
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?

See The Solution Submitted by Jer    
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  Subject Author Date
an answer to 1 thru 6Dej Mar2011-08-03 03:08:48
Some ThoughtsA start, with 1 and 2 (spoilers for these), and a thoughtCharlie2011-08-01 14:00:06
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