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.
2019-12-17
@
Rob
: It looks to me like you've made mistakes in questions 1, 6, 8, and 9. The hints from the back of the pdf might help:
1.
How many numbers between 1 and 10,000 have 1 as their final digit? How many have 1 as their penultimate digit?
6.
How many ways can you write 1? 2? 3? 4? 5? What's the pattern?
8.
How many zeros does 10! end in? How many zeros does 20! end in? How many zeros does 30! end in?
9.
Carol’s sum is odd. What does this tell you about the 5- and 6-digit numbers?
Matthew
on
/blog/70
×4
×3
×4
×3
×4
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
wave scattering
dates
a gamut of games
weather station
bots
crossnumber
gather town
arrangement puzzles
hats
crochet
sport
national lottery
the aperiodical
logo
boundary element methods
ternary
squares
convergence
pokémon wordle
cambridge
royal institution
error bars
kenilworth
oeis
electromagnetic field
recursion
geometry
noughts and crosses
data
pac-man
pascal's triangle
realhats
people maths
puzzles
plastic ratio
anscombe's quartet
menace
dinosaurs
sobolev spaces
matrices
newcastle
triangles
coins
turtles
sound
exponential growth
fence posts
map projections
draughts
rhombicuboctahedron
correlation
big internet math-off
stickers
hyperbolic surfaces
zines
flexagons
bubble bobble
manchester science festival
inline code
graph theory
game show probability
alphabets
bluesky
misleading statistics
light
curvature
tmip
numerical analysis
mathsteroids
news
braiding
stirling numbers
books
python
databet
polynomials
guest posts
finite element method
cross stitch
tetris
arithmetic
propositional calculus
machine learning
runge's phenomenon
programming
pizza cutting
gerry anderson
probability
pythagoras
video games
raspberry pi
standard deviation
golden ratio
mathsjam
accuracy
reuleaux polygons
dragon curves
captain scarlet
hannah fry
harriss spiral
friendly squares
bempp
sorting
determinants
pi approximation day
speed
matrix of cofactors
javascript
asteroids
advent calendar
statistics
chebyshev
kings
final fantasy
nonograms
warwick
weak imposition
matrix of minors
coventry
datasaurus dozen
world cup
latex
youtube
tennis
trigonometry
royal baby
european cup
folding tube maps
finite group
thirteen
matt parker
fractals
chalkdust magazine
simultaneous equations
approximation
christmas card
24 hour maths
interpolation
christmas
frobel
martin gardner
game of life
errors
graphs
manchester
estimation
football
wordle
live stream
golden spiral
talking maths in public
crosswords
reddit
geogebra
regular expressions
rust
go
ucl
games
matrix multiplication
fonts
data visualisation
dataset
computational complexity
radio 4
quadrilaterals
preconditioning
palindromes
edinburgh
craft
logic
binary
countdown
numbers
logs
signorini conditions
hexapawn
gaussian elimination
php
mathslogicbot
pokémon
bodmas
london underground
inverse matrices
platonic solids
partridge puzzle
phd
wool
rugby
folding paper
london
chess
nine men's morris
crossnumbers
mean
pi
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
bluesky
game of life
weather station
latex
squares
databet
crochet
24 hour maths
thirteen
sorting
polynomials
big internet math-off
weak imposition
computational complexity
edinburgh
video games
news
php
fonts
cross stitch
chebyshev
plastic ratio
triangles
bodmas
rugby
raspberry pi
regular expressions
golden spiral
phd
the aperiodical
palindromes
london underground
runge's phenomenon
alphabets
martin gardner
craft
signorini conditions
determinants
flexagons
javascript
cambridge
european cup
datasaurus dozen
dinosaurs
live stream
arithmetic
dataset
map projections
python
coventry
pythagoras
countdown
menace
chalkdust magazine
final fantasy
boundary element methods
pokémon
convergence
harriss spiral
preconditioning
nonograms
books
statistics
stirling numbers
sport
pac-man
data
gerry anderson
inline code
logic
matt parker
pi
rhombicuboctahedron
probability
matrices
mean
numerical analysis
hexapawn
graphs
guest posts
a gamut of games
go
bempp
zines
matrix of minors
noughts and crosses
bots
approximation
gather town
asteroids
crosswords
errors
pascal's triangle
kings
realhats
golden ratio
trigonometry
coins
programming
electromagnetic field
recursion
ucl
stickers
folding tube maps
talking maths in public
gaussian elimination
wave scattering
tetris
bubble bobble
mathsteroids
games
game show probability
logo
youtube
christmas
hannah fry
football
fractals
reuleaux polygons
oeis
finite group
propositional calculus
reddit
estimation
dates
friendly squares
pizza cutting
geometry
data visualisation
speed
inverse matrices
matrix of cofactors
exponential growth
hats
arrangement puzzles
braiding
radio 4
newcastle
pi approximation day
christmas card
crossnumbers
hyperbolic surfaces
manchester science festival
rust
accuracy
kenilworth
anscombe's quartet
curvature
warwick
platonic solids
error bars
standard deviation
chess
logs
ternary
fence posts
numbers
sobolev spaces
matrix multiplication
frobel
folding paper
manchester
misleading statistics
binary
sound
crossnumber
correlation
turtles
captain scarlet
advent calendar
puzzles
national lottery
tmip
machine learning
mathslogicbot
royal baby
dragon curves
nine men's morris
wool
royal institution
london
interpolation
draughts
graph theory
tennis
world cup
mathsjam
finite element method
partridge puzzle
wordle
people maths
geogebra
quadrilaterals
light
pokémon wordle
simultaneous equations
© Matthew Scroggs 2012–2026
1. How many numbers between 1 and 10,000 have 1 as their final digit? How many have 1 as their penultimate digit?
6. How many ways can you write 1? 2? 3? 4? 5? What's the pattern?
8. How many zeros does 10! end in? How many zeros does 20! end in? How many zeros does 30! end in?
9. Carol’s sum is odd. What does this tell you about the 5- and 6-digit numbers?
on /blog/70