Mastodawn

A friend has sent me an interesting meta-puzzle, but we need to start with the first one.

Attached is a black and white figure divided into four regions. That challenge is to divide the white regions into 2, 3, 4, and 5 congruent pieces.

More explicitly, one of the white regions will be subdivided into 2 congruent regions. Another into 3, and so on.

Can you find a solution?

The second phase will follow later, but I think this is interesting enough in its own right.

Please put solutions and spoilers behind a CW.

PS: Classical methods and constructions only. We're in Puzzle World, not Crypto World.

#RecMaths #RecMath #Math #Maths #MathsPuzzle #MathPuzzle #Geometry #GeometryPuzzle

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MOULE

Apr 25, 2025

UPDATE: My program found a new personal best most delayed palindromic number!

The 25-digit number 1102320000659911613429286 takes 235 iterations before it becomes a 123-digit palindrome.

This beats a former world record set in 2003 by Jason Doucette involving 233 iterations (source: https://jasondoucette.com/worldrecords.html#Most), and is 58 iterations off from the current world record of 293.

#Math #LychrelNumber #MostDelayedPalindromicNumber #Mathematics #RecMath #RecreationalMathematics

Jason Doucette - World Records - 196 Palindrome Quest, Most Delayed Palindromic Number

Jason Doucette's Resume Homepage, World Records for Interesting Mathematical Patterns involving Numerical Palindromes, Yarmouth Co., Nova Scotia, Canada.

MOULE

Apr 17, 2025

((10^n)-1)*(2/3)-53, a formula resulting in rows of n number of sixes with the last two sixes replaced with the number 13, result in primes for n = 2, 3, 7, 12, 30, 97, 192, 265, 327, 417, 475, 574, 595, 699, 9563, and 9601.

Update: It's ran for 10 days and hasn't found any other new primes below n = 37000. Stopping the program now!

#Math #Mathematics #PrimeNumbers #RecreationalMath #RecMath #RecreationalMathematics #Primes

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MOULE

Apr 13, 2025

Update: New record! After appending random digit after random digit for two days, it eventually found this 31689-digit prime. It's larger than the 148091th number in the Fibonacci sequence, which is also prime.

The tiny white digits on the black background look like TV static when zoomed out!

#Math #Mathematics #PrimeNumbers #Primes #RecreationalMathematics #RecMath

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MOULE

Apr 12, 2025

Update: overnight it found a 17828-digit prime number, a new personal best!

I can see why most primes found are found with easy-to-write formulae like (2^p)-1 or (k^2^n)+1. Ttrying to go backwards – coming up with a compact formula to represent a really huge prime made up of random digits like this one, is really tricky.

#Math #Mathematics #PrimeNumbers #Primes #RecreationalMathematics #RecMath

MOULE

Apr 11, 2025

Just for fun, I wrote a Python program to start with a random decimal digit, and keep adding the decimal digit until it reaches a prime number.

I'm excited to share it's found a 10997-digit long prime number, which is my new personal best largest prime! It's larger than the 37th factorial prime (3507!-1) which is 10912 digits.

I'll leave the program running overnight to see if it can find longer ones!

#Math #Mathematics #PrimeNumbers #Primes #RecreationalMathematics #RecMath