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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
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Christmas card 2025
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Christmas (2025) is coming!
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The partridge puzzle
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TMiP 2025 puzzle hunt
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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!
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Zines, pt. 2
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Christmas (2023) is over
2023
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Dec 2023
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Christmas (2023) is coming!
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Chalkdust issue 17
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Logo Asteroids
Mar 2023
Mathsteroids on hyperbolic surfaces
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The databet
Jan 2023
Christmas (2022) is over
2022
▼ show ▼
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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 -15+3τ-φ-√3 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
european cup
noughts and crosses
mean
fonts
final fantasy
propositional calculus
friendly squares
christmas
guest posts
javascript
matt parker
manchester
the aperiodical
cambridge
computational complexity
chalkdust magazine
boundary element methods
preconditioning
inverse matrices
tennis
weather station
error bars
bubble bobble
determinants
raspberry pi
london underground
hyperbolic surfaces
christmas card
graph theory
go
menace
numbers
warwick
hexapawn
fractals
people maths
platonic solids
bots
mathsjam
tmip
logs
tetris
royal institution
errors
live stream
correlation
thirteen
golden spiral
kenilworth
wave scattering
alphabets
gaussian elimination
matrices
data
php
runge's phenomenon
exponential growth
probability
bodmas
realhats
chess
pi
gerry anderson
video games
hannah fry
game of life
turtles
partridge puzzle
crochet
accuracy
signorini conditions
pokémon wordle
rhombicuboctahedron
kings
inline code
recursion
manchester science festival
london
books
puzzles
geometry
bluesky
binary
datasaurus dozen
convergence
quadrilaterals
crosswords
asteroids
football
fence posts
folding paper
matrix multiplication
logic
standard deviation
anscombe's quartet
databet
wordle
python
pizza cutting
wool
logo
speed
regular expressions
numerical analysis
braiding
approximation
programming
national lottery
latex
martin gardner
nine men's morris
hats
sport
coventry
crossnumbers
plastic ratio
dates
phd
estimation
mathsteroids
advent calendar
countdown
ternary
harriss spiral
reuleaux polygons
newcastle
trigonometry
game show probability
stickers
dataset
pac-man
sobolev spaces
pi approximation day
folding tube maps
gather town
edinburgh
games
statistics
palindromes
stirling numbers
golden ratio
machine learning
dragon curves
frobel
misleading statistics
zines
craft
coins
bempp
sorting
big internet math-off
rugby
data visualisation
ucl
news
24 hour maths
reddit
matrix of cofactors
dinosaurs
triangles
nonograms
pokémon
weak imposition
electromagnetic field
chebyshev
talking maths in public
polynomials
finite group
interpolation
arithmetic
geogebra
curvature
matrix of minors
youtube
radio 4
royal baby
map projections
draughts
sound
graphs
rust
pascal's triangle
flexagons
crossnumber
pythagoras
simultaneous equations
oeis
light
squares
finite element method
a gamut of games
captain scarlet
cross stitch
arrangement puzzles
mathslogicbot
world cup
© 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