[ image courtesy of Futility Closet ]
Here’s an interesting puzzle named the spider and the fly, from Henry Ernest Dudeney (via Futility Closet):
Inside a rectangular room, measuring 30 feet in length and 12 feet in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, as at A, and a fly is on the opposite wall, 1 foot from the floor in the centre, as shown at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? Of course the spider never drops or uses its web, but crawls fairly.
This puzzle was posted yesterday by Greg Ross, and he promised that he would publish the solution today. I am looking forwards to that. Greg classified this puzzle as “tricky”. I would not classify it as “tricky”, but rather as “not-so-obvious”. After some reasoning, one should be able to come up with a solution (which may not be unique).
I will await for Greg’s solution and comment on it. I will then present my own solution to the general case problem, and attempt to show you that this problem is deeper and richer than it may appear at first sight.
April 3, 2007 at 20:55 |
There is a related family of questions that place the spider in the corner between two walls, but a foot off the ceiling, and the spider the opposite intersection, but a foot off the floor. Will your solution cover those places.
April 3, 2007 at 21:40 |
Thanks for your input Jonathan!
In fact, I had not considered the possibility of having the spider in the corner between two walls, but the solution I thought of can handle those cases pretty well. I’m glad.
I will address these topics in an upcoming post. I still have to “play” a bit more with this problem before I feel comfortable to publish my solution in this blog. There’s nothing worse than looking like a total idiot in front of everyone just because I didn’t do my “homework” properly.