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# Mathematical BafflersMarch 1965 Mechanix Illustrated

 March 1965 Mechanix Illustrated Wax nostalgic about and learn from the history of early mechanics. See articles from Mechanix Illustrated, published 1928 - 2001. All copyrights hereby acknowledged.

Mathematical Bafflers, by Angela Dunn

This March 1965 issue of Mechanix Illustrated is part of a huge boxful of vintage magazines I picked up at a local estate sale for \$20. It also included Popular Mechanics, Science & Mechanics, and a few others. All of them were on my regular reading list back in the 1970 and 1980s. I have been going through them looking for useful content for "RF Cafe" and for my "Airplanes and Rockets" website. A book review was done for Mathematical Bafflers, by Angela Dunn. To whet readers' appetites, a few examples appeared, along with their solutions, all of which are provided here. A search of the Internet turned up a PDF copy of the entire Mathematical Bafflers book, in case you are interested in such things - which you probably are if you've read this far. I have to admit that even with reading the solution, I still do not understand Q1. For Q2, I first made a simple guess based on the stated bricklaying rates of the two workers, and got the correct number on the first try (pure luck, I'm sure). A bit of cogitating was enough to get Q3 (no equations involved). Update: I just figured out what Ms. Dunn was looking for in Q1, but I still never would have guessed it. Hint: It refers to the sum of the products of the numbers, which can include exponents - they add up to exactly 100.

## Mathematical Bafflers

Mathematical Bafflers compiled by Angela Dunn: 217 pages: price \$6.50. McGraw-Hill, New York.

For you insatiable puzzlers, there's another puzzle book out. There being no better way to introduce it or help you evaluate it than to slip you a few samples, here goes:

The Maximal Product

What is the largest number which can be obtained as the product of positive integers which add up to 100?

The Bricklayers

A contractor estimated that one of his two bricklayers would take 9 hours to build a certain wall and the other 10 hours. However, he knew from experience that when they worked together, 10 fewer bricks got laid per hour. Since he was in a hurry, he put both men on the job and found it took exactly 5 hours to build the wall. How many bricks did it contain?

An Unusual Year

The year 1961 had the rare property of reading the same upside-down. Of how many years (A.D.) has this been true, and how many more will elapse before another?

Quizzes from vintage electronics magazines such as Popular Electronics, Electronics-World, QST, and Radio News were published over the years - some really simple and others not so simple. Robert P. Balin created most of the quizzes for Popular Electronics. This is a listing of all I have posted thus far.

Solutions

Clearly 1 would not appear as a factor, and any 4 could be replaced by two 2s, without decreasing the product. And if one of the factors were greater than 4, replacing it by 2 and n-2 would yield a larger product. Thus the factors are all 2s and 3s. Moreover, not more than two 2s are used, since the replacement of three 2s by two 3s would increase the product. The largest number possible is therefore 332 x 22.

Let N = number of bricks in wall, N/9 = number of bricks first bricklayer lays per hour, N/10 = number of bricks second bricklayer lays per hour, N/9 + N/10 - 10 = number of bricks laid per hour when they work together, and finally N/ (N/9 + N/10 - 10) = 5, from which n = 900.

It has been true 23 times since and including the year zero. However, over 4000 years more must elapse until the next occurrence, which takes place in 6009.

Posted September 28, 2023