Math genius John Conway dies from COVID-19

[Doctor Q]

One of my personal heroes, John Conway, has died at age 82.

He was an amazing mathematician, a teacher, an inventor, a magician, and a great thinker. He was best known for inventing the wonderful Game of Life, played with on-off states on an infinite grid:

I've written a few programs to play the Game of Life myself. One particular type of cell layout produces a "glider gun," which is a stable pattern that churns out new patterns called gliders. Gliders, in turn, move across the grid by replicating themselves in a shifted position.

Conway was responsible for many other math advances too, across so many fields: number theory, quantum mechanics, group theory, geometry, algebra, topology, and more.

He got the idea for the Game of Life while pondering how machines could replicate themselves:

 

[jkcerda]

We've Come Up With 20 Brand-New Riddles to Test Your Critical Thinking and Logic Skills

Looking for incredibly challenging riddles? Try all of our tough new brain teasers that combine logic and math to test your mental mettle. No cheating!

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have fun with it

“Dear Virginia,

Little did I know when I headed to work this Monday morning, that by evening we would have a beautiful baby girl. And on our wedding anniversary, no less! It makes me think back to that incredible weekend day, J___ 27th, 19___, when we first shared our vow to create a family together, and, well, here we are! Happy eighth anniversary, my love.

Love, Edwin”

The question: When was Carol’s mother born?

Hint
This problem is inspired by Conway’s Doomsday Rule.

Solution
Ready for the solution? Click here to see if you're right.

To Solve This Twisty Math Riddle, You Just Need One Belt and One Earth

(Difficulty: Moderate)

Imagine you have a very long belt. Well, extremely long, really … in fact, it’s just long enough that it can wrap snugly around the circumference of our entire planet. (For the sake of simplicity, let’s suppose Earth is perfectly round, with no mountains, oceans, or other barriers in the way of the belt.)

Naturally, you’re very proud of your belt. But then your brother, Peter, shows up—and to your disgruntlement, he produces a belt that’s just a bit longer than yours. He brags his belt is longer by exactly his height: 6 feet.

If Peter were also to wrap his belt around the circumference of Earth, how far above the surface could he suspend the belt if he pulled it tautly and uniformly?

Hint
Earth’s circumference is about 25,000 miles, or 130 million feet … but you don’t need to know that to solve this problem.

 

[PracticalMac]

He was best known for inventing the wonderful Game of Life, played with on-off states on an infinite grid:

According to the rules, a straight line of squares would neither die (2 adjacent squares alive) nor reproduce (no 3ed square to trigger another square to become alive), thus stagnation.

But if 1 live square hits the line, an atomic reaction occurs.

Correct?

(been decades since I tried that, on Win 3.1)

 

[Doctor Q]

A straight line of squares will change quite a bit. Although the initial squares will remain for one generation (i.e., one application of the rules), the squares on the end of the line will die from starvation (only 1 neighbor each, unless you're imagining an infinite line) so the line will shrink from both ends.

More importantly, the squares immediately above and below the line will be born since each of those squares has 3 neighbors. That will then kill the initial squares from overcrowding (neighbors next to, above, and below). Continued growth will be in an approximate diamond shape. I think you'll eventually end up in a steady state of beehives, blinkers, or traffic lights, but I don't know if that's guaranteed for any initial number of blocks.