To test a new robot, two hundred smooth white stones are placed 3 feet apart in a long straight line on the ground. A basket is placed at the beginning of the line, 3 feet away from the first stone. The robot starts at the basket and collects the stones one by one, putting each stone in the basket before going to get the next stone. The robot never moves the basket. It takes quite awhile. How far does the robot travel? (And what is the robot's name?)
Solution
Distances traveled out and back:
stone #
- 3 + 3 = 6
- 6 + 6 = 12
- 9 + 9 = 18
and so on, until
- 600 + 600 = 1200.
Total: 6 + 12 + 18 + ... + 1200 = 6(1 + 2 + 3 + ... + 200)
= 6(200 x 201)/2 = 3 x 200 x 201 = 120,600 feet, or 22.84 miles.
(And a student suggested that the robot's name is Miles.)
