mscroggs.co.uk
mscroggs.co.uk

subscribe

Comment

Comments

Comments in green were written by me. Comments in blue were not written by me.
@selina
Good instinct to start with smaller variants of the problem and working your way up.

You've chosen a perhaps confusing way of directly tackling the big length=14 problem, by partitioning it as "how big is the set of 14-digit numbers with exactly that many 2s".

Note that you can start smaller and simpler, by just considering shorter-length numbers first.

As you work the shorter examples, you may see a pattern in construction, or a pattern in the numbers. Either intuition will help you.
Dr Matrix
on /blog/97
×2   ×1   ×1   ×1   ×1   

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

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

Archive

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