Joe Doodlebug is an imaginary, and somewhat strange, bug, These are his capabilities and limitations in his world.
1. His world is flat.
2. He can only jump (not crawl, fly, walk, roll, or otherwise move across or under the surface of his world).
3. He cannot turn around.
4. He can jump very large distances or very small distances, but not less than one inch per jump nor more than 500 feet per jump
5. He can jump in only four perfectly true directions-north, south, east, and west. He cannot jump diagonally (e.g., southeast, northwest)
6. He likes to average 15 feet per jump on a good day.
7. There are no other doodlebugs, or other creatures, to help him.
8. Once he starts in any direction, he must jump four times in that same direction before he can switch to another direction.
9. Joe is totally dependent on his owner to provide his food source.
Joe has been out jumping all over the place while getting some much-needed exercise. As a matter of fact, Joe has worked up a voracious appetite. Much to his pleasure, his owner appears and places a large pile of delectable food 3 feet, 7 inches directly west of him. Joe wants the food, and he wants it fast. As soon as Joe sees all this wonderful food, he stops dead in his tracks (he is facing north), After all his exercise he is very hungry, and even weak. Therefore, he wants to get to the food as quickly as he possibly can, minimizing especially the number of jumps he makes (it's the starting of a jump-the spring required in his legs-that
takes the most energy). After briefly surveying the situation, he realizes that he cannot-at this point-jump due west. Suddenly he exclaims, "I've got it. l'll only have to jump four times to get to the food!"
Accept the fact that Joe was a smart bug, and dead right in his conclusions.
Why did Joe Doodlebug have to take precisely four jumps in order to reach the food with a minimum expenditure of energy? Describe the circumstances that Joe must have been in to reach this conclusion.