mscroggs.co.uk
mscroggs.co.uk

subscribe

Comment

Comments

Comments in green were written by me. Comments in blue were not written by me.
I would appreciate a hint for puzzle 23. I am struggling to derive a recurrence relation or formula. How to find the pattern for number of ways?
Reza
on /blog/107
×1   ×1   ×1   ×1   ×1   
@Reza:

I didn't use a recurrence. When dividing into three areas, one of the the lines must span the entire grid creating two areas. Then one more line is used to split one of the just created areas into three areas. I just figured out how many ways there are to place the first line, then how many ways there are to place the second. There are two main scenarios you need to deal with:
1) Two horizontal or vertical lines
2) One horizontal and one vertical line

Hope that helps
Aaron
on /blog/107
×4   ×1   ×2   ×2   ×2   
@Aaron: Wow thank you Aaron, that was just the idea I needed. Very fun.
Reza
on /blog/107
×3   ×3   ×3   ×3   ×3   

Archive

Show me a random blog post
 2026 

May 2026

World Cup stickers 2026

Apr 2026

A new puzzle every day
Mixing Wordle with other games

Feb 2026

Christmas (2025) is over
 2025 

Dec 2025

Christmas card 2025

Nov 2025

Christmas (2025) is coming!

Sep 2025

The partridge puzzle

Aug 2025

TMiP 2025 puzzle hunt

Jun 2025

A nonogram alphabet

Mar 2025

How to write a crossnumber

Jan 2025

Christmas (2024) is over
Friendly squares
 2024 

Dec 2024

A regular expression Christmas puzzle
Christmas card 2024

Nov 2024

Christmas (2024) is coming!

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

convergence databet recursion simultaneous equations trigonometry geometry bempp mean 24 hour maths cambridge plastic ratio dates graph theory logo palindromes pizza cutting manchester fractals determinants wave scattering gather town dataset pokémon wordle interpolation rugby errors news ternary arithmetic alphabets chebyshev gerry anderson frobel royal institution signorini conditions computational complexity hexapawn javascript noughts and crosses pascal's triangle accuracy people maths nine men's morris game of life polynomials golden spiral youtube binary mathslogicbot coventry bluesky quadrilaterals mathsteroids hats folding tube maps tennis dragon curves oeis matrix of cofactors mathsjam coins menace world cup guest posts edinburgh pokémon matrices boundary element methods propositional calculus crossnumber inverse matrices numbers harriss spiral raspberry pi anscombe's quartet phd go thirteen european cup friendly squares machine learning electromagnetic field books a gamut of games pi approximation day numerical analysis probability matt parker exponential growth warwick christmas bodmas craft data wordle fence posts turtles rhombicuboctahedron sound curvature golden ratio martin gardner approximation puzzles matrix of minors talking maths in public tmip bots flexagons live stream braiding inline code advent calendar hyperbolic surfaces latex stickers big internet math-off pac-man tetris countdown draughts sobolev spaces programming final fantasy games ucl zines crossnumbers map projections captain scarlet platonic solids misleading statistics london asteroids arrangement puzzles dinosaurs sorting folding paper radio 4 stirling numbers kenilworth speed php reuleaux polygons logs triangles python error bars matrix multiplication light wool weather station fonts pi datasaurus dozen hannah fry runge's phenomenon nonograms regular expressions data visualisation football sport crosswords reddit gaussian elimination standard deviation partridge puzzle game show probability preconditioning newcastle royal baby graphs the aperiodical logic weak imposition christmas card video games estimation rust finite group kings realhats manchester science festival chalkdust magazine crochet pythagoras national lottery statistics finite element method squares chess bubble bobble london underground correlation cross stitch geogebra

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2026