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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
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×3
×4
×3
×4
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Christmas (2025) is coming!
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A nonogram alphabet
Mar 2025
How to write a crossnumber
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Christmas (2024) is over
Friendly squares
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A regular expression Christmas puzzle
Christmas card 2024
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Christmas (2024) is coming!
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Christmas (2023) is coming!
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Logo Asteroids
Mar 2023
Mathsteroids on hyperbolic surfaces
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The databet
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▼ show ▼
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Dec 2022
Off-by-one errors
Christmas card 2022
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Christmas (2022) is coming!
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24 Hour Maths Game Show
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Approximating π
Feb 2022
Build your own MENACE
Jan 2022
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▼ show ▼
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Dec 2021
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Christmas (2021) is coming!
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TMiP 2021 puzzle hunt
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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 -4+τ 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
numbers
pythagoras
warwick
pascal's triangle
polynomials
rhombicuboctahedron
fonts
matrices
alphabets
python
folding paper
matrix of minors
frobel
dates
sobolev spaces
squares
signorini conditions
coventry
data visualisation
gather town
christmas card
approximation
tetris
noughts and crosses
christmas
matt parker
geogebra
triangles
youtube
arrangement puzzles
programming
radio 4
binary
finite group
raspberry pi
logic
wordle
hannah fry
crossnumber
statistics
stirling numbers
curvature
pizza cutting
sorting
error bars
dinosaurs
nine men's morris
correlation
tmip
guest posts
reuleaux polygons
coins
propositional calculus
errors
reddit
golden ratio
friendly squares
game of life
partridge puzzle
craft
ucl
cambridge
sport
javascript
kings
plastic ratio
games
weather station
simultaneous equations
arithmetic
realhats
crochet
data
matrix multiplication
machine learning
puzzles
cross stitch
light
bubble bobble
mathsteroids
hexapawn
24 hour maths
platonic solids
datasaurus dozen
map projections
estimation
mathslogicbot
gaussian elimination
latex
turtles
ternary
national lottery
final fantasy
geometry
mathsjam
oeis
preconditioning
logo
chalkdust magazine
convergence
royal baby
flexagons
manchester
bluesky
logs
runge's phenomenon
rugby
books
wool
sound
hats
determinants
go
hyperbolic surfaces
newcastle
stickers
pokémon wordle
live stream
pi
probability
chebyshev
interpolation
fractals
finite element method
the aperiodical
menace
bodmas
graphs
mean
nonograms
harriss spiral
numerical analysis
palindromes
london
crosswords
manchester science festival
matrix of cofactors
pac-man
martin gardner
rust
game show probability
boundary element methods
fence posts
dataset
edinburgh
asteroids
regular expressions
crossnumbers
folding tube maps
phd
video games
braiding
inline code
kenilworth
php
misleading statistics
graph theory
inverse matrices
talking maths in public
accuracy
countdown
draughts
thirteen
royal institution
recursion
exponential growth
zines
european cup
weak imposition
bots
anscombe's quartet
chess
trigonometry
quadrilaterals
databet
tennis
wave scattering
dragon curves
world cup
speed
a gamut of games
standard deviation
football
london underground
pi approximation day
news
pokémon
people maths
golden spiral
captain scarlet
computational complexity
big internet math-off
electromagnetic field
bempp
advent calendar
gerry anderson
© 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