In each issue of the Automation Notebook we feature a section of brainteasers. These are the brainteaser answers from Issue 5, 2005 of the Automation Notebook. The brainteaser questions are repeated in black. The answers to the brainteaser questions are highlighted in red with explanations. You can view the brainteasers from Issue 5, 2005 without the answers here: http://library.automationdirect.com/brainteasers-issue-5-2005/
1. Walking in Circles
A classic puzzle describes the hunter who walks a mile south, turns and walks a mile east, turns again and walks a mile north. He is surprised to find himself right back where he started. He then shoots a bear. What color is the bear? The answer is usually given as “white”, because the hunter must have started his 3 mile walk at the North Pole. Can you find some other places on the globe where you could follow those same directions and end up at your starting point?
Hint: No polar bears near any of those places!
Answer: Walking in Circles Other than at the north pole, there are quite a few other places on the globe where you can walk a mile south, a mile east, a mile north, and be back where you started. For example: If you were 1.159 miles north of the south pole (anywhere on that circle), then when you walk the one mile south you would be 0.159 mile from the pole. This is exactly the right distance (radius) from the pole, so that your “one mile east” trek will take you exactly once around the pole. Then, of course, when you turn and walk your “one mile north” you will be retracing your steps from the first leg of your journey. Now consider starting at 1.08 miles north of the south pole. This would offer you the opportunity to loop the south pole twice before retracing your steps. These distances are an interesting progression. 1.159 is more accurately 1 plus (1 over 2pi). 1.08 is 1 plus (1 over 4pi), the list goes on for 3 trips around the pole, start at 1 + (1 over 6pi) miles, and so forth. For each of these distances from the south pole,technically there are an infinite number of starting points along the circle. But you won’t see any bears this close to the south pole!
2. Out of Sight
Fred has designed a new machine for the factory where he works. His design was followed perfectly, but he forgot to specify the order, and the labels, for four light switches on the control console. These four on-off switches are wired to four ordinary light bulbs on the far end of the machine—out of sight from the control panel. He knows that each switch is correctly wired to one of the lights. He knows that all the bulbs are new and working, and he even knows the on and off position of the switches, but he doesn’t know which light is connected to each switch.
Fred’s boss is on the way out to the factory floor to see a demonstration of the machine, but Fred must determine how the switches and lights are wired before he can give a successful demonstration. He only has time for one trip down to the far end of the machine where the lights are mounted. How can Fred determine which switch controls each light in a single trip without anyone to help him?
Answer: Walking in Circles Other than at the north pole, there are quite a few other places on the globe where you can walk a mile south, a mile east, a mile north, and be back where you started. For example: If you were 1.159 miles north of the south pole (anywhere on that circle), then when you walk the one mile south you would be 0.159 mile from the pole. This is exactly the right distance (radius) from the pole, so that your “one mile east” trek will take you exactly once around the pole. Then, of course, when you turn and walk your “one mile north” you will be retracing your steps from the first leg of your journey. Now consider starting at 1.08 miles north of the south pole. This would offer you the opportunity to loop the south pole twice before retracing your steps. These distances are an interesting progression. 1.159 is more accurately 1 plus (1 over 2pi). 1.08 is 1 plus (1 over 4pi), the list goes on for 3 trips around the pole, start at 1 + (1 over 6pi) miles, and so forth. For each of these distances from the south pole,technically there are an infinite number of starting points along the circle. But you won’t see any bears this close to the south pole!