Mind Matters News is pleased to offer a new series, “Monday Micro Softies,” from our director, Robert J. Marks, a series of puzzles that illustrate the ways of thinking needed in the computer industry today. – Eds.

The answer to last week’s brain teaser on baseball averages is below but first, here’s a new Micro Softy about haircuts.

I live in McGregor, Texas. It’s a small town with only one traffic light.

Assume there are two barbers in McGregor and no other barbers within a radius of five hundred miles. New to McGregor, I need to choose a barber. I want a friendly barber who can discreetly deemphasize my thinning hair and receding hairline.

On my first visit McVeigh’s Barber Shop, I am impressed. McVeigh looks professional in his spotless white smock. He is clean-shaven and well-groomed. He sports a neatly trimmed mustache and every hair on his head is in place. His small one-chair shop is clean and tidy. There are two men waiting, reading magazines, while McVeigh begins cutting the hair of a third.

Next I visit Garcia’s barber shop. Garcia’s clothes look like he slept in them. He has a two-day growth of beard stubble, and his uneven hair looks greasy and not well combed.  He chomps on the stub of an unlit cigar while he cuts the hair of a sole customer. I ask about prices and find out that Garcia charges less than McVeigh for a haircut.

Since there is no other barber within 500 miles, I am stuck choosing between Garcia and McVeigh. Who should I choose and why?

Solution to Micro Softy 7:  Who’s the Champ?

I wrote about this type of problem back in 2019. It’s an illustration of Simpson’s Paradox, which says that averaging averages doesn’t always work.

A player’s batting average is the number of hits divided by the number of at-bats.

From the more detailed batting average table shown, Babe had a better batting average than Mickey for both the months of April and May. But for the combined months of April and May, Mickey has a better batting average, namely 470 to Babe’s 350. The numbers in the table don’t lie.

In each individual month, Babe did better than Mickey. But, as is seen in the table for the combined two months, Mickey was the winner.

So the takeaway is this: Be wary of averages of averages:

Here are the Micro Softies from earlier Mondays, to date. The answer to one Monday’s puzzle is always given the next Monday:

Monday Micro Softy 1: Microsoft: What did you need to work there in the early days? They asked questions that were not about the details of computer technology. The questions made you think. Hard. For example, they would ask questions like, why are manhole covers round? Also, here’s the Round Trip puzzle.

Monday Micro Softy 2: The Dead Presidents’ Club The answer to Monday Micro Softy 1: The Round Trip puzzle is here too. Today’s puzzle: How would a girl who knew nothing of American history immediately know the name of at least one of three early Presidents who died on July 4?

Monday Micro Softy 3: The Wolverton Mountain Puzzle Here’s the answer to Dead President’s Club as well — and smart STEM people often DON’T get that one right. Today’s brain teaser is in honor of Claude King, Clifton Clowers, and Wolverton Mountain. It’s not high tech but it will surely test your thinking abilities.

Monday Micro Softy 4: Claude King bests Clifton Clowers Clowers offers Claude two slips of paper to choose from on a blind choice: marriage or death… Claude’s sweetheart Chloe warns him that, in reality, both slips say “death.” He says never mind. So how did he escape death and marry her?

Monday Micro Softy 5: The puzzle of Claude and Chloe’s two kids Puzzle: We learn that one of Claude and Chloe’s two children is a boy. With a 50–50 ratio, what chance is there that the other child is a boy too? Also, here’s the answer to the puzzle of how, twelve years earlier, Claude escaped the trap Clifton Clowers set for him, so he could marry Chloe.

Monday Micro Softy 6: Bad Adding? It looked to Claude like young Clay’s numbers didn’t add up but the boy seemed confident. What did he know that his father at first didn’t?And here’s the answer to the probability question: What are the chances that Claude and Chloe’s younger child is also a boy?

Monday Micro Softy 7: Who’s the Champ? A single number does not always determine which player is better. And here’s the answer to why young Clay’s arithmetic didn’t make sense at first to Claude — but then Claude realized that the boy was right.