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Monday Micro Softy 9: To Flip or Not to Flip?

Probability theory can sometimes help with seemingly impossible questions. But how?
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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 solution to Micro Softy 8, Who’s the Better Barber? is below. But first , here’s #9, to further tickle your brain:

Picture three cards turned face down. Each has a dollar amount written on it. The amount can be anything from a penny to millions of dollars. The first card, chosen at random, is turned over. You have the choice of keeping the amount on the card or ripping it up and turning over a second card. You choose to look.

Again, you can keep the amount on the second card, rip it up, and turn over the last card.  But the last card you turn over is the one you keep.

There’s a catch. You can only walk away with the amount shown on a card if it’s the largest dollar amount of all three cards. Otherwise, you win nothing.

What strategy should you use to maximize the chance you walk away with money? And what percent of the time do you walk away with money?

We’ll give the answer in the next Micro Softy posting here next Monday at Mind Matters News!

And now here’s the solution to Micro Softy 8:  Who’s the Better Barber?

A vintage, rustic barber shop sign hangs prominently outside an establishment on a quaint street, evoking a nostalgic atmosphere from a bygone era

The problem is this. McGregor, Texas, has two barbers. There are no other barbers within 500 miles. McVeigh is a neatnik with perfect hair and Garcia is a slob with bad hair. Since McVeigh must cut Garcia’s hair and Garcia must cut McVeigh’s hair, choose Garcia. He gave McVeigh a great haircut. McVeigh, on the other hand, gave Garcia a bad haircut.

So Garcia is the better barber.

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.

Monday Micro Softy 8: Who’s the better barber? There are only two barbers to choose from and the choice may not be as easy as it looks. Also, here’s the answer to Who’s the Champ? Micro Softy 7 is an illustration of Simpson’s Paradox, which says that averaging averages doesn’t always work.


Monday Micro Softy 9: To Flip or Not to Flip?