Mind Matters Natural and Artificial Intelligence News and Analysis

CategoryLogic

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Interlocking triangles in primary colors layered with precision

Monday Micro Softy 26: Arguing with Pythagoras

Will the diagonal of a triangle with sides of 3 and 4 feet be 5 feet or, as a visiting mathematician suggests, 7 feet?
The answer to last week’s puzzle lies in remembering what happens when you put a rod on a diagonal inside a square box. Read More ›
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Hand made wood burn tic tac toe game with painted rock game pieces; yellow and red beetles and a wooden x and o game, sunset light

Micro Softy Monday 24: Have You Ever Tried 3D Tic Tac Toe?

To liven up a predictable game, try doing it in three — or even four — dimensions! You won't be bored
To solve the Barnum's Circus ticket receipts puzzle, recall that X, Y and Z must all be whole numbers. Algebra then enables us to work out the solution. Read More ›
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Circus lion. Ai art

Monday Micro Softy 23: Barnum’s Circus Receipts

Circus master Barnum's ticket seller had not kept proper track of the tickets sold. Can the limited information — and some algebra — help Barnum figure it out?
The solution to Micro Softy 22, given here, depends on the assumptions we make about Timmy's surgeon. Read More ›
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Multiple brown medicine bottles filled with yellow pills are arranged in a row on a reflective surface, creating a visually appealing composition

Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills

The solution to last week's deadly pills puzzle can be found, as we'll see, by numbering the bottles. But this week we make the challenge tougher…
In this week’s challenge, you don’t know how many pill bottles, if any, have been laced with fentanyl. Can you still discover the truth with a single weighing? Read More ›
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Abstract geometric background with triangles

Monday Micro Softy 19: The “Bermuda Triangle”

Why does the strange triangle, rearranged, appear to have a bit of extra area?
The solution to the Twins Paradox lies in considering the possibility that Curt and Rod were not alone in the womb. Read More ›
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Three fabric gift bags in gray, beige, and red, sitting on a marble surface against a bokeh background of Christmas lights.

Monday Micro Softy 17: Mixed-up Bags of Marbles

The bags-of-marbles puzzle is comparatively simple: How many marbles must you pull from the mislabeled bags in order to relabel them correctly?
There’s a rough solution to the “leaky bucket” problem but an exact solution requires some use of fluid dynamics. And the Moon, surprisingly, changes nothing. Read More ›
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Colorful space galaxy cloud nebula. Stary night cosmos. Universe science astronomy. Supernova background wallpaper

Ross Douthat Makes the Case that Religious Belief Is Rational

His new book is written largely with the agnostic or full-on atheist in mind but believers would certainly also benefit, as I did
He notes, if our brains evolved merely to help us stay alive, then it’s strange that those same mental states could invent the telescope to explore the cosmos. Read More ›
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Set of metal washers in the foreground

Micro Softy 15: What Happens to the Hole in a Hot Washer?

When a washer ring is heated, does the hole in the center get bigger or smaller?
The answer to last week’s Micro Softy turns on the question of what form of currency Claire gave the blind ticket seller. Did you guess it right? Read More ›
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Facade of Grand Central Terminal at twilight in New York

Monday Micro Softy 14: How Did the Blind Ticket Seller Know?

This puzzle doesn’t require math skills so much as advanced common sense reasoning
About last week’s solution, given here: If you code, the second part of the puzzle could also be offered to a computer. Read More ›
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Sandcastle at St Aubin's Beach

How Mathematician Kurt Gödel Proved the Unprovable Proposition

He kicked over the mathematical sandcastles of those who proposed a mathematical Theory of Everything
While Gödel’s technique was unheard of in his day, we are very familiar with it today. It is the same technique that computers use to store information. Read More ›
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stained-glass window

Monday Micro Softy 13: Garbage Trucks, String Theory…

… and Stained-Glass Windows. What connects them?
These puzzles, associated with the great mathematician Leonard Euler (1707‒1783), have a practical use, for example, in laying water pipes. Read More ›
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group of musicians after the performance of his work

Monday Micro Softy 11: What Happened to That Other Dollar?

Shirley, Goodness, and Mercy get the discount for their cheap hotel rooms but the figures don’t really add up
To solve this Micro Softy, you need to pinpoint the flaw in the logic that hinges on the Law of Conservation of Money. Read More ›
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Manhole drain cover on streets of lower Manhattan

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? Read More ›
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Four-leaf clover stands out against green leaves

Bad Luck Seldom Persists — But it Never Guarantees Good Luck

Many people embrace the fallacious law of averages in their daily lives when "regression toward the mean" is a more realistic picture
For example, the baseball player with the highest batting average in any season generally does not do as well the season before or the season after. Read More ›