mscroggs
.co.uk
mscroggs
.co.uk
blog
puzzles
academic
talks
contact
subscribe
↓ ☰ ↓
subscribe
Loading image...
Comment
Comments
Comments in green were written by me. Comments in blue were not written by me.
2025-12-18
Is there a word missing (positive?) from Q9? Surely any positive integer, n, can be written as the sum of the consecutive integers -(n-1),...,-1,0,1,...,n-1,n.
Alec
on
/blog/121
2025-12-18
@
Alec
: Yes, it should say positive integers
Matthew
on
/blog/121
×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 ▼
▲ hide ▲
Dec 2023
Christmas card 2023
Nov 2023
Christmas (2023) is coming!
Zines
Sep 2023
TMiP 2023 puzzle hunt
May 2023
Chalkdust issue 17
Apr 2023
Logo Asteroids
Mar 2023
Mathsteroids on hyperbolic surfaces
Feb 2023
The databet
Jan 2023
Christmas (2022) is over
2022
▼ show ▼
▲ hide ▲
Dec 2022
Off-by-one errors
Christmas card 2022
Nov 2022
Christmas (2022) is coming!
Oct 2022
24 Hour Maths Game Show
Mar 2022
Approximating π
Feb 2022
Build your own MENACE
Jan 2022
Christmas (2021) is over
2021
▼ show ▼
▲ hide ▲
Dec 2021
Christmas card 2021
Nov 2021
Christmas (2021) is coming!
Sep 2021
TMiP 2021 puzzle hunt
May 2021
Close encounters of the second kind
Jan 2021
Christmas (2020) is over
2020
▼ show ▼
▲ hide ▲
Dec 2020
Christmas card 2020
Nov 2020
Christmas (2020) is coming!
Jul 2020
Happy -26+eg Approximation Day!
May 2020
A surprising fact about quadrilaterals
Interesting tautologies
Mar 2020
Log-scaled axes
Feb 2020
PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2
Jan 2020
PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
2019
▼ show ▼
▲ hide ▲
Dec 2019
Visualising MENACE's learning
Christmas card 2019
Nov 2019
Christmas (2019) is coming!
Sep 2019
A non-converging LaTeX document
TMiP 2019 treasure punt
Jul 2019
Big Internet Math-Off stickers 2019
Jun 2019
Proving a conjecture
Apr 2019
Harriss and other spirals
Mar 2019
realhats
Jan 2019
Christmas (2018) is over
2018
▼ show ▼
▲ hide ▲
Dec 2018
Christmas cross stitch
MENACE in fiction
Christmas card 2018
Nov 2018
Christmas (2018) is coming!
Sep 2018
Runge's Phenomenon
Jul 2018
World Cup stickers 2018, pt. 3
Mathsteroids
Jun 2018
World Cup stickers 2018, pt. 2
May 2018
A bad Puzzle for Today
Apr 2018
Building MENACEs for other games
Mar 2018
A 20,000-to-1 baby?
World Cup stickers 2018
Jan 2018
Origins of World War I
Christmas (2017) is over
2017
▼ show ▼
▲ hide ▲
Dec 2017
Christmas card 2017
Nov 2017
Christmas (2017) is coming!
MENACE at Manchester Science Festival
Jun 2017
Big Ben Strikes Again
Mar 2017
The end of coins of constant width
Dragon curves II
Feb 2017
The importance of estimation error
Jan 2017
Is MEDUSA the new BODMAS?
2016
▼ show ▼
▲ hide ▲
Dec 2016
Christmas (2016) is over
Video game surfaces
Christmas card 2016
Nov 2016
Christmas (2016) is coming!
Oct 2016
Logical contradictions
Palindromic dates
Sep 2016
Tube map kaleidocycles
Jul 2016
Solving the cross diagonal cover problem
Jun 2016
Braiding, pt. 2
Braiding, pt. 1
Making names in Life
May 2016
Euro 2016 stickers
Mar 2016
Proving Pythagoras' theorem
Dragon curves
The
Mathematical Games
of Martin Gardner
Jan 2016
Christmas (2015) is over
2015
▼ show ▼
▲ hide ▲
Nov 2015
Christmas (2015) is coming!
Oct 2015
How to kick a conversion
How much will I win on the new National Lottery?
Aug 2015
How OEISbot works
MENACE
Mar 2015
Optimal Pac-Man
Tube map stellated rhombicuboctahedron
Logic bot, pt. 2
Design your own flexagon
Jan 2015
Tube map Platonic solids, pt. 3
2014
▼ show ▼
▲ hide ▲
Nov 2014
Logic bot
Sep 2014
Electromagnetic Field talk
Jun 2014
Tennis maths
May 2014
World Cup stickers
Apr 2014
Countdown probability, pt. 2
Countdown probability
Mar 2014
New machine unfriendly £1 coin, pt. 2
New machine unfriendly £1 coin
2013
▼ show ▼
▲ hide ▲
Dec 2013
Assorted christmaths
Pointless probability
Jul 2013
"Uncanny" royal coincidence
Raspberry Pi weather station
2012
▼ show ▼
▲ hide ▲
Nov 2012
Tube map Platonic solids, pt. 2
Oct 2012
Tube map Platonic solids
Tags
pac-man
logo
runge's phenomenon
graph theory
bodmas
pizza cutting
reuleaux polygons
oeis
thirteen
weather station
national lottery
pi approximation day
tetris
statistics
signorini conditions
games
people maths
mathsjam
correlation
plastic ratio
chess
reddit
logic
simultaneous equations
map projections
edinburgh
frobel
noughts and crosses
datasaurus dozen
game of life
matrix of minors
bluesky
radio 4
misleading statistics
mean
big internet math-off
programming
nonograms
puzzles
flexagons
weak imposition
arrangement puzzles
cross stitch
stickers
mathsteroids
recursion
trigonometry
manchester science festival
football
logs
phd
palindromes
royal institution
turtles
alphabets
latex
computational complexity
crossnumber
matrix multiplication
sobolev spaces
coins
stirling numbers
approximation
pokémon
python
guest posts
gather town
data visualisation
data
craft
cambridge
kings
errors
game show probability
newcastle
asteroids
error bars
royal baby
crosswords
exponential growth
sorting
finite element method
platonic solids
draughts
machine learning
geometry
martin gardner
partridge puzzle
php
hexapawn
javascript
sport
menace
standard deviation
wave scattering
realhats
squares
final fantasy
go
crossnumbers
triangles
probability
polynomials
warwick
rust
boundary element methods
live stream
crochet
hats
pascal's triangle
chalkdust magazine
inverse matrices
golden ratio
london
propositional calculus
numerical analysis
fence posts
rugby
folding paper
youtube
friendly squares
finite group
london underground
bots
coventry
quadrilaterals
estimation
advent calendar
video games
dinosaurs
electromagnetic field
ucl
world cup
chebyshev
countdown
tennis
kenilworth
bempp
european cup
pokémon wordle
a gamut of games
regular expressions
gaussian elimination
matrix of cofactors
mathslogicbot
fonts
databet
tmip
curvature
pi
interpolation
dataset
sound
gerry anderson
nine men's morris
convergence
numbers
wordle
binary
captain scarlet
graphs
dragon curves
arithmetic
matt parker
speed
24 hour maths
folding tube maps
hannah fry
inline code
golden spiral
fractals
dates
news
manchester
the aperiodical
bubble bobble
ternary
harriss spiral
books
preconditioning
zines
christmas card
light
pythagoras
determinants
talking maths in public
wool
geogebra
anscombe's quartet
rhombicuboctahedron
raspberry pi
braiding
matrices
accuracy
hyperbolic surfaces
christmas
Archive
Show me a random blog post
▼ show ▼
▲ hide ▲
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 ▼
▲ hide ▲
Dec 2023
Christmas card 2023
Nov 2023
Christmas (2023) is coming!
Zines
Sep 2023
TMiP 2023 puzzle hunt
May 2023
Chalkdust issue 17
Apr 2023
Logo Asteroids
Mar 2023
Mathsteroids on hyperbolic surfaces
Feb 2023
The databet
Jan 2023
Christmas (2022) is over
2022
▼ show ▼
▲ hide ▲
Dec 2022
Off-by-one errors
Christmas card 2022
Nov 2022
Christmas (2022) is coming!
Oct 2022
24 Hour Maths Game Show
Mar 2022
Approximating π
Feb 2022
Build your own MENACE
Jan 2022
Christmas (2021) is over
2021
▼ show ▼
▲ hide ▲
Dec 2021
Christmas card 2021
Nov 2021
Christmas (2021) is coming!
Sep 2021
TMiP 2021 puzzle hunt
May 2021
Close encounters of the second kind
Jan 2021
Christmas (2020) is over
2020
▼ show ▼
▲ hide ▲
Dec 2020
Christmas card 2020
Nov 2020
Christmas (2020) is coming!
Jul 2020
Happy -26+eg Approximation Day!
May 2020
A surprising fact about quadrilaterals
Interesting tautologies
Mar 2020
Log-scaled axes
Feb 2020
PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2
Jan 2020
PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
2019
▼ show ▼
▲ hide ▲
Dec 2019
Visualising MENACE's learning
Christmas card 2019
Nov 2019
Christmas (2019) is coming!
Sep 2019
A non-converging LaTeX document
TMiP 2019 treasure punt
Jul 2019
Big Internet Math-Off stickers 2019
Jun 2019
Proving a conjecture
Apr 2019
Harriss and other spirals
Mar 2019
realhats
Jan 2019
Christmas (2018) is over
2018
▼ show ▼
▲ hide ▲
Dec 2018
Christmas cross stitch
MENACE in fiction
Christmas card 2018
Nov 2018
Christmas (2018) is coming!
Sep 2018
Runge's Phenomenon
Jul 2018
World Cup stickers 2018, pt. 3
Mathsteroids
Jun 2018
World Cup stickers 2018, pt. 2
May 2018
A bad Puzzle for Today
Apr 2018
Building MENACEs for other games
Mar 2018
A 20,000-to-1 baby?
World Cup stickers 2018
Jan 2018
Origins of World War I
Christmas (2017) is over
2017
▼ show ▼
▲ hide ▲
Dec 2017
Christmas card 2017
Nov 2017
Christmas (2017) is coming!
MENACE at Manchester Science Festival
Jun 2017
Big Ben Strikes Again
Mar 2017
The end of coins of constant width
Dragon curves II
Feb 2017
The importance of estimation error
Jan 2017
Is MEDUSA the new BODMAS?
2016
▼ show ▼
▲ hide ▲
Dec 2016
Christmas (2016) is over
Video game surfaces
Christmas card 2016
Nov 2016
Christmas (2016) is coming!
Oct 2016
Logical contradictions
Palindromic dates
Sep 2016
Tube map kaleidocycles
Jul 2016
Solving the cross diagonal cover problem
Jun 2016
Braiding, pt. 2
Braiding, pt. 1
Making names in Life
May 2016
Euro 2016 stickers
Mar 2016
Proving Pythagoras' theorem
Dragon curves
The
Mathematical Games
of Martin Gardner
Jan 2016
Christmas (2015) is over
2015
▼ show ▼
▲ hide ▲
Nov 2015
Christmas (2015) is coming!
Oct 2015
How to kick a conversion
How much will I win on the new National Lottery?
Aug 2015
How OEISbot works
MENACE
Mar 2015
Optimal Pac-Man
Tube map stellated rhombicuboctahedron
Logic bot, pt. 2
Design your own flexagon
Jan 2015
Tube map Platonic solids, pt. 3
2014
▼ show ▼
▲ hide ▲
Nov 2014
Logic bot
Sep 2014
Electromagnetic Field talk
Jun 2014
Tennis maths
May 2014
World Cup stickers
Apr 2014
Countdown probability, pt. 2
Countdown probability
Mar 2014
New machine unfriendly £1 coin, pt. 2
New machine unfriendly £1 coin
2013
▼ show ▼
▲ hide ▲
Dec 2013
Assorted christmaths
Pointless probability
Jul 2013
"Uncanny" royal coincidence
Raspberry Pi weather station
2012
▼ show ▼
▲ hide ▲
Nov 2012
Tube map Platonic solids, pt. 2
Oct 2012
Tube map Platonic solids
Tags
london underground
matrix of minors
rust
zines
hyperbolic surfaces
sobolev spaces
harriss spiral
graph theory
matt parker
gerry anderson
final fantasy
javascript
propositional calculus
royal baby
books
sport
menace
mathsteroids
inline code
sound
noughts and crosses
cambridge
programming
london
games
braiding
game of life
gaussian elimination
guest posts
polynomials
platonic solids
triangles
coins
fonts
golden ratio
light
mean
stirling numbers
big internet math-off
misleading statistics
trigonometry
matrix of cofactors
numerical analysis
asteroids
dataset
boundary element methods
pi approximation day
electromagnetic field
craft
the aperiodical
nonograms
pokémon wordle
alphabets
christmas card
finite element method
partridge puzzle
advent calendar
computational complexity
graphs
weather station
accuracy
statistics
manchester science festival
rugby
mathsjam
data visualisation
sorting
kenilworth
stickers
ucl
error bars
interpolation
crossnumber
dinosaurs
fence posts
dates
mathslogicbot
hexapawn
speed
rhombicuboctahedron
geogebra
martin gardner
quadrilaterals
cross stitch
bots
nine men's morris
map projections
tetris
chalkdust magazine
inverse matrices
finite group
approximation
a gamut of games
binary
crossnumbers
recursion
tennis
friendly squares
radio 4
pi
crochet
estimation
national lottery
chebyshev
simultaneous equations
flexagons
captain scarlet
game show probability
latex
pokémon
newcastle
data
chess
pac-man
php
hats
pythagoras
draughts
pascal's triangle
turtles
coventry
geometry
arithmetic
christmas
world cup
pizza cutting
logo
manchester
reuleaux polygons
puzzles
royal institution
realhats
machine learning
live stream
errors
thirteen
go
talking maths in public
golden spiral
numbers
datasaurus dozen
databet
runge's phenomenon
python
oeis
edinburgh
dragon curves
crosswords
kings
european cup
bempp
bubble bobble
warwick
exponential growth
hannah fry
youtube
palindromes
squares
reddit
wool
arrangement puzzles
weak imposition
matrix multiplication
frobel
matrices
folding paper
folding tube maps
standard deviation
football
raspberry pi
correlation
24 hour maths
bluesky
plastic ratio
determinants
signorini conditions
logs
preconditioning
regular expressions
tmip
wave scattering
convergence
probability
wordle
curvature
bodmas
gather town
news
fractals
ternary
logic
phd
people maths
video games
anscombe's quartet
countdown
© Matthew Scroggs 2012–2026
on /blog/121