Mind Matters Natural and Artificial Intelligence News and Analysis

CategoryMathematics

a-collage-of-baseball-players-and-memorabilia-stockpack-adob-1010320881-stockpack-adobestock
A Collage of Baseball Players and Memorabilia

Monday Micro Softy 55: “It Happens Every Spring”

Baseball, that is. Here’s a puzzle that takes in baseball's favorite season, summer
To solve last week’s puzzle, you don’t need to know the distance. Check the problem again for the number you do need to know. Read More ›
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Two Commercial Airliners Pass Each Other at High Altitude

Micro Softy 54: A Plane Problem for Aspiring Engineers

The senator is leaving Washington to avoid the governor and their planes are headed in opposite directions

Today’s Micro Softy tests whether you are clever enough with math to code computers or be an engineer. Here’s the story: Senator Kornn did not like Governor Friar. Both were from Texas. When Kornn learned that Governor Friar was visiting Washington, DC, Kornn said “This town’s not big enough for the both of us.”  So Kornn decided to leave DC for that period. Kornn and Friar get on planes at the same time. One was at Reagan International Airport in DC and the other was at the Dallas Fort Worth (DFW) Airport. So each was flying to the other’s airport. Both planes took off at the same time. After a while, Kornn looked out of his first-class window and saw Read More ›

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Protecting Balance Between Percentage And House Model

Home Ownership: Madness Over 30-Year Mortgages

It is tempting to put borrowing and investment decisions in separate mental buckets, but they are intimately related
When considering a mortgage, the correct comparison is not total payments but the return on the borrowed money versus the loan’s annual percentage rate. Read More ›
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Empty driveway in front of the big white luxury dream house in the evening. Residential home building exterior, expensive dwelling, wealthy rich family property and yard. Glowing mansion

Monday Micro Softy 53: Kicking In the Door

To solve this puzzle, you will need to sharpen your abductive reasoning skills
There are actually two possible solutions to last week's puzzle, depending on how you interpret the pattern of the arithmetic. Read More ›
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A pile of light bulbs, one bulb is glowing bright while the others are dark can symbolize creative thinking or innovative ideas being born from simple concepts Generative AI

Monday Micro Softy 52: Elon Musk Parody Asks: Are You a Genius?

The puzzle comes from a parody X account but it is a genuine stumper
Last week’s puzzle is easy to solve if we recall how many parents a child needs and of what type… Read More ›
male-mechanic-hold-and-rolling-tire-at-repairing-service-gar-286788620-stockpack-adobestock
Male mechanic hold and rolling tire at repairing service garage background. Technician man replacing winter and summer tyre for safety road trip. Transportation and automotive maintenance concept

Monday Micro Softy 51: A Tale of Two Auto Mechanics

I recognized the two mechanics when I went to the garage…
To solve Microsofty 50, about cutting a loaf of cornbread into eight pieces by making three slices, try thinking in three dimensions. Read More ›
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Delicious, golden, and fluffy cornbread pieces, artfully stacked, enticing a feeling of warmth and comfort

Monday Micro Softy 50: Cutting Through the Cornbread

How did Yuri Senior cut the cornbread into eight identical portions using only three straight cuts?
You can guess the answer to Microsofty 49 if you try the test question yourself at home, using a small mirror. Read More ›
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grand central

Monday Micro Softy 46: Three Loving Brothers in New York State

Why did Mario, who was just trying to economize on Uber trips, end up visiting Luigi five times as often as he visited Bob?
A hint for solving Micro Softy 45: Average speed is independent of the distance to the store. Read More ›
a-futuristic-fast-food-joint-stands-tall-its-walls-of-gleami-966802437-stockpack-adobestock
A futuristic fast food joint stands tall, its walls of gleaming metal and glass illuminated by a dazzling

Monday Micro Softy 45: Can Tony Beat the Fast-Food Curfew?

An early curfew on fast food service motivated a boy to exercise more vigorously. But how fast was he pedaling?
To solve Micro Softy 44, recall that Tony doesn’t need to take the individual pills each day, only the prescribed amount of each. Read More ›
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Tiny tropical island with hut and palms surrounded sea blue water, generative AI.

Micro Softy 44:  Pete’s Pill Problem

Pete, alone on a desert island, accidentally scattered the pills he must take in the correct order. He has only a few numbers to work with to reconstruct his instructions
For Micro Softy 43, the bookkeeper’s trick consists in applying the fact that when two adjacent digits are switched, the difference is always divisible by 9. Read More ›
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Microscopic View of Bacteria Cells with Flagella on Organic Surface

Monday Micro Softy 42: Bacteria Multiply by Dividing

But our puzzlers must solve this math question without doing either. And no calculators allowed.
A hint for solving Micro Softy 41: Dividing an unusually shaped piece of land among four sons rather than three is easier if you think in terms of fractals. Read More ›
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colorful geometric paper squares background

Monday Micro Softy 41: King David’s Sons’ Puzzling Inheritance

Solomon must figure out how to divide an oddly shaped piece of land equally among his brothers and himself
In Micro Softy 40, the critical question is not whether the watchman’s prophecy comes true or not; it’s how he came to learn the information anyway. Read More ›
a-mesmerizing-illustration-of-mathematics-featuring-a-vibran-1278627221-stockpack-adobestock
A mesmerizing illustration of mathematics featuring a vibrant swirling vortex of numbers symbols and geometric shapes in shades of electric blue crimson and gold set against a rich dark gray backgroun

Is AI Truly Creative? Here Is the Ultimate Test

People use the term “creative” in different ways. We need to define it rigorously and use a test based on that agreed definition
AI does not, at present, originate the kind of deep insight required to solve a open mathematical problem. Read More ›
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Closeup of Baseball Glove and Baseball on turf

Monday Micro Softy 37: A Unique Baseball Game

Something was missing from the game played on June 30, 1997, that occured in every MLB game for decades before
The answer to Micro Softy 36 lies in considering the problem from a number of angles… Read More ›
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Desert Locust on Sand Dune with Green Vegetation in Arid Environment

Monday Micro Softy 36: A Glass Half Empty? Half Full? Too Big?

The professors on a research expedition must make sure that each glass of rationed water is exactly half full

Here’s our thirst-quenching Micro Softy for this week. Three professors were on a trip through the Sahara Desert. They had an NSF grant to study the sleep patterns of the Saharan Grasshopper (Heteracris littoralis).  They brought exactly enough drinking water with them to last for four days. To stay hydrated, each was allowed a half glass of water every hour during each sixteen-hour workday. The professors shared the water glass shown in the picture. To make sure the water lasted the entire four days, the professors made sure each portion of water filled the glass exactly halfway. There were no markings on the glass. How can they do this? We’ll give an answer next Monday right here on MindMatters.ai.    Solution Read More ›

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Montana

Monday Micro Softy 35: A House With a View

A billionaire, used to getting what he wants, demands a house where all the walls' windows offer a view in the same direction
The solution to Monday Micro Softy 34 is quite simple if we pay attention to the exact measurements of the poles and the wires. Read More ›
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Mathematics lesson differential and integral calculus Chalkboard.

Monday Micro Softy 32: Elementary Calculus is Inconsistent!

This is a fascinating puzzle — one that usually stumps even my best graduate students
The solution to Micro Softy 31 is to work back from the end of the alphabet. You will soon notice a term you can easily solve. Read More ›