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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?

See answers below.

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.

 RF Cafe Quizzes RF Cafe Quiz #71: Tech Headlines for Week of 3/13/2023 RF Cafe Quiz #70: Analog & RF Filter Basics RF Cafe Quiz #69: RF Electronics Basics RF Cafe Quiz #68: RF & Analog Company Mergers & Acquisitions in 2017 RF Cafe Quiz #67: RF & Microwave Company Name Change History RF Cafe Quiz #66: Spectrum and Network Measurements RF Cafe Quiz #65: Troubleshooting & Repairing Commercial Electrical Equipment RF Cafe Quiz #64: Space-Time Adaptive Processing for Radar RF Cafe Quiz #63: Envelope Tracking Power Amplifiers RF Cafe Quiz #62: Stimson's Introduction to Airborne Radar RF Cafe Quiz #61: Practical Microwave Circuits RF Cafe Quiz #60: Ten Essential Skills for Electrical Engineers RF Cafe Quiz #59: Microwave Circulator Design RF Cafe Quiz #58: Microwave and Millimeter-Wave Electronic Packaging RF Cafe Quiz #57: Frequency-Agile Antennas for Wireless Communications RF Cafe Quiz #56: Tube Testers and Electron Tube Equipment RF Cafe Quiz #55: Conquer Radio Frequency RF Cafe Quiz #54: Microwave Mixer Technology and Applications RF Cafe Quiz #53: Chipless RFID Reader Architecture RF Cafe Quiz #52: RF and Microwave Power Amplifiers RF Cafe Quiz #51: Antennas and Site Engineering for Mobile Radio Networks RF Cafe Quiz #50: Microstrip Lines and Slotlines RF Cafe Quiz #49: High-Frequency Integrated Circuits RF Cafe Quiz #48: Introduction to Infrared and Electro-Optical Systems RF Cafe Quiz #47: LCP for Microwave Packages and Modules RF Cafe Quiz #46: RF, Microwave, and Millimeter-Wave Components RF Cafe Quiz #45: Dielectric and Thermal Properties of Materials at Microwave Frequencies RF Cafe Quiz #44: Monopulse Principles and Techniques RF Cafe Quiz #43: Plasma Antennas RF Cafe Quiz #42: The Micro-Doppler Effect in Radar RF Cafe Quiz #41: Introduction to RF Design Using EM Simulators RF Cafe Quiz #40: Introduction to Antenna Analysis Using EM Simulation RF Cafe Quiz #39: Emerging Wireless Technologies and the Future Mobile Internet RF Cafe Quiz #38: Klystrons, Traveling Wave Tubes, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons RF Cafe Quiz #37: Component Reliability for Electronic Systems RF Cafe Quiz #36: Advanced RF MEMS RF Cafe Quiz #35: Frequency Synthesizers: Concept to Product RF Cafe Quiz #34: Multi-Gigabit Microwave and Millimeter-Wave Wireless Communications RF Cafe Quiz #33: Battlespace Technologies: Network-Enabled Information Dominance RF Cafe Quiz #32: Modern Communications Receiver Design and Technology RF Cafe Quiz #31: Quantum Mechanics of Nanostructures RF Cafe Quiz #30: OFDMA System Analysis and Design RF Cafe Quiz #29: Cognitive Radar RF Cafe Quiz #28: Human-Centered Information Fusion RF Cafe Quiz #27: Remarkable Engineers RF Cafe Quiz #26: Substrate Noise Coupling in Analog/RF Circuits RF Cafe Quiz #25: Component Reliability for Electronic Systems RF Cafe Quiz #24: Ultra Low Power Bioelectronics RF Cafe Quiz #23: Digital Communications Basics RF Cafe Quiz #22: Remember the Basics? RF Cafe Quiz #21: Wireless Standards Knowledge RF Cafe Quiz #20: Famous First Names RF Cafe Quiz #19: Basic Circuit Theory RF Cafe Quiz #18: Archaic Scientific Words & Definitions RF Cafe Quiz #17: Inventors & Their Inventions RF Cafe Quiz #16: Antennas RF Cafe Quiz #15: Numerical Constants RF Cafe Quiz #14: Oscillators RF Cafe Quiz #13: General Knowledge RF Cafe Quiz #12: Electronics Corporations Headquarters RF Cafe Quiz #11: Famous Inventors & Scientists RF Cafe Quiz #10: A Sampling of RF & Wireless Topics RF Cafe Quiz #9: A Smorgasbord of RF Topics RF Cafe Quiz #8: Hallmark Decades in Electronics RF Cafe Quiz #7: Radar Fundamentals RF Cafe Quiz #6: Wireless Communications Fundamentals RF Cafe Quiz #5: Company Logo Recognition RF Cafe Quiz #4: General RF Topics RF Cafe Quiz #3: General RF/Microwave Topics RF Cafe Quiz #2: General RF Topics RF Cafe Quiz #1: General RF Knowledge Vacuum Tube Quiz, February 1961 Popular Electronics Kool-Keeping Kwiz, June 1970 Popular Electronics Find the Brightest Bulb Quiz, April 1960 Popular Electronics Where Do the Scientists Belong? - Feb 19, 1949 Saturday Evening Post Vintage Electronics Magazine Quizzes Quiz on AC Circuit Theory, December 1970 Popular Electronics Magnetic Phenomena Quiz, February 1962 Popular Electronics Electronics Geography Quiz, April 1970 Popular Electronics Electronic Menu Quiz, August 1963 Popular Electronics Electronic Noise Quiz, August 1962 Popular Electronics Electronic Current Quiz, October 1963 Popular Electronics Electronic Inventors Quiz, November 1963 Popular Electronics Resistor Function Quiz, January 1962 Popular Electronics Electronic Measurement Quiz, January 1963 Popular Electronics Vintage Electronics Magazine Quizzes What's Your EQ? - June 1962 Radio-Electronics What's Your EQ? - April 1967 Radio-Electronics What's Your EQ? - March 1967 Radio-Electronics What's Your EQ? - December 1964 Radio-Electronics What's Your EQ? - January 1967 Radio-Electronics Wanted: 50,000 Engineers - January 1953 Popular Mechanics What's Your EQ? - August 1964 Radio-Electronics Voltage Quiz - December 1961 Popular Electronics What is It? -  June 1941 Popular Science What Do You Know About Resistors? - April 1974 Popular Electronics What's Your EQ? - September 1963 Radio-Electronics Potentiometer Quiz - September 1962 Popular Electronics Mathematical Bafflers - March 1965 Mechanix Illustrated Op Amp Quiz - October 1968 Popular Electronics Electronic "A" Quiz - April 1968 Popular Electronics What's Your EQ? - May 1961 Radio-Electronics Popular Science Question Bee - February 1939 Popular Science What is It? - A Question Bee in Photographs - June 1941 Popular Science What's Your EQ? - June 1961 Radio-Electronics What's Your EQ? - June 1964 Radio-Electronics What's Your EQ? - May 1964 Radio-Electronics What's Your EQ? - August 1963 Radio-Electronics What's Your EQ? - May 1963 Radio-Electronics Bridge Function Quiz - September 1969 Radio-Electronics What's Your EQ? - March 1963 Radio-Electronics What's Your EQ? - February 1967 Radio-Electronics Circuit Quiz - June 1966 Radio-Electronics What's Your EQ? - June 1966 Radio-Electronics Electronics Mathematics Quiz - June 1969 Popular Electronics Brightest Light Quiz - April 1964 Popular Electronics What's Your EQ? - April 1963 Radio-Electronics Electronics "B" Quiz - July 1969 Popular Electronics Ohm's Law Quiz - March 1969 Popular Electronics Antenna Quiz - November 1962 Electronics World Color Code Quiz - November 1967 Popular Electronics CapaciQuiz - August 1961 Popular Electronics Transformer Winding Quiz - December 1964 Popular Electronics Audiophile Quiz - November 1957 Radio-electronics Capacitor Function Quiz - March 1962 Popular Electronics Greek Alphabet Quiz - December 1963 Popular Electronics Circuit Designer's Name Quiz - July 19680 Popular Electronics Sawtooth Sticklers Quiz - November 1960 Radio-Electronics Elementary Radio Quiz - December 1947 Radio-Craft Hi-Fi Quiz - October 1955 Radio & Television News Electronics Physics Quiz - March 1974 Popular Electronics A Baffling Quiz - January 1968 Popular Electronics Electronics IQ Quiz - May 1967 Popular Electronics Plug and Jack Quiz - December 1967 Popular Electronics Electronic Switching Quiz - October 1967 Popular Electronics Electronic Angle Quiz - September 1967 Popular Electronics International Electronics Quiz - July 1967 Popular Electronics FM Radio Quiz - April 1950 Radio & Television News  Bridge Circuit Quiz -December 1966 Popular Electronics Diode Function Quiz - August 1965 Popular Electronics Diagram Quiz, August 1966 Popular Electronics Quist Quiz - November 1953 QST TV Trouble Quiz, July 1966 Popular Electronics Electronics History Quiz, December 1965 Popular Electronics Scope-Trace Quiz, March 1965 Popular Electronics Electronic Circuit Analogy Quiz, April 1973 Test Your Knowledge of Semiconductors, August 1972 Popular Electronics Ganged Switching Quiz, April 1972 Popular Electronics Lamp Brightness Quiz, January 1969 Popular Electronics Lissajous Pattern Quiz, September 1963 Popular Electronics Electronic Quizoo, October 1962 Popular Electronics Electronic Photo Album Quiz, March 1963 Popular Electronics Electronic Alphabet Quiz, May 1963 Popular Electronics Quiz: Resistive? Inductive? or Capacitive?, October 1960 Popular Electronics Vector-Circuit Matching Quiz, June 1970 Popular Electronics Inductance Quiz, September 1961 Popular Electronics RC Circuit Quiz, June 1963 Popular Electronics Diode Quiz, July 1961 Popular Electronics Electronic Curves Quiz, February 1963 Popular Electronics Electronic Numbers Quiz, December 1962 Popular Electronics Energy Conversion Quiz, April 1963 Popular Electronics Coil Function Quiz, June 1962 Popular Electronics Co-Inventors Quiz - January 1965 Electronics World "-Tron" Teasers Quiz - October 1963 Electronics World Polarity Quiz - March 1968 Popular Electronics Television I.Q. Quiz - October 1948 Radio & Television News Amplifier Quiz Part I - February 1964 Popular Electronics Semiconductor Quiz - February 1967 Popular Electronics Unknown Frequency Quiz - September 1965 Popular Electronics Electronics Metals Quiz - October 1964 Popular Electronics Electronics Measurement Quiz - August 1967 Popular Electronics Meter-Reading Quiz, June 1966 Popular Electronics Electronic Geometry Quiz, January 1965 Popular Electronics Electronic Factor Quiz, November 1966 Popular Electronics Electronics Math Quiz, November 1965 Popular Electronics Series Circuit Quiz, May 1966 Popular Electronics Electrochemistry Quiz, March 1966 Popular Electronics Biz Quiz: Test Your Sales Ability - April 1947 Radio News Electronic Analogy Quiz, November 1961 Popular Electronics Electronic Coupling Quiz, August 1973 Popular Electronics Electronics Analogy Quiz, August 1960 Popular Electronics Audio Quiz, April 1955 Popular Electronics Electronic Unit Quiz, May 1962 Popular Electronics Capacitor Circuit Quiz, June 1968 Popular Electronics

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

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