Smith, Robert (ed.) / The Wisconsin engineer
Volume 69, Number 7 (April 1965)
Fonstad, Clifton, Jr.
The mental maze, pp. 28 ff.
THE MEN TAL MAZE By CLIFTON FONSTAD, JR. ee4 APHIL means that you have only this one more chance to win a Maze Master award this year. Next month's answers will be given after the problems and there will be no May Maze Master. So that you can get to the puzzles quickly then, we'll cut the words of wisdom short and simply make note of the fact that the Mental Maze is just packed with illustrations and good puzzles to go with them this month. Now, let's get started on the first puzzle-the first turn in this months Mental Maze. 1. The first puzzle is one for the industrial engineers. Anyone can work it though so have a go at it. If a tinker and his helper can refabulate a widgit in 2 days, and if the tinker working with his apprentice instead would take 3 days, while the helper and the apprentice would take 6 days to do the job, how long would it take each working alone to re- fahulate the widgit? 2. Here's an interesting problem sent down from a fan at Tioga Tech. One of the landmarks on the Tech campus is a large tower with a clock at the top. This clock tolls out the hours as regularly today as it did fifty years ago but it has changed some. When the clock was installed it took it eight seconds to strike eight; now it takes six seconds to strike six. Our question is-how many sec- onds does it take the clock to strike twelve? How long did it take originally? 3. If you're still with us and didn't get tricked too badly by the last couple turns in the maze see if you can get past this next one. 28 Suppose you want to construct the following figure out of match- sticks. In the center is a square with an integral number of match- sticks on each side. Then using each side of the square as a base four triangles are constructed- each is different and each has sides made with an integral num- ber of matchsticks. The result looks like the diagram below where a, b, c, are integers repre- senting the number of matcbsticks in each line. What is the minimum number of matchsticks that can be used to form such a figure? b S C- -f h 4. The last puzzle might have taken a while so let's try a couple shorter ones. In a domino set that runs up to double-six, there are 28 pieces or bones. In a set that runs up to double-nine there are 55 bones. How many bones are there in a domino set that runs up to double- twelve? Who would want a domino set that big? 5. Now, for those of you with money here is a coin shuffing prob- lem. Start out with four pennies and four nickels placed alternately in a row as shown below. * @ 0 @ 0 00 * e o o o o 0 One move is made by moving any two adjacent coins together to another position on the line. Make four such moves and rear- range the coins in a line so that all the pennies and all the nickels are together as shown in the sec- ond drawing. 6. To close out April's maze try playing with a little Algebra. There are three computers in the basement of the Lesser Antilles and Farther North Studies Build- ing on campus. Computer A is as old as computers B and C to- gether. Last year B was twice as old as C and in two vears com- puter A will be twice as old as computer C. How old are the three computers? ANSWERS The answers to last month's Mental Maze are: 1. 2/5 2. 54,45 years 3. 70 yards 13485_ 13845 _ 14865 2697 2769 2973 18645 - 3729 5. 5 men 6. 416 pages This is your last chance to win a Maze Master award and the five dollars that goes with it because next month we have to publish the answers with the Maze. So hurry and send your solutions to the Mental Maze, Wisconsin Engi- neer, 333 Mechanical Engineering, University of Wisconsin, Madison. Remember, too, you don't have to have all the correct answers to win. THE WISCONSIN ENGINEER
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