mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2024-12-04 
As usual, I spent some time this November, designing this year's Chalkdust puzzle Christmas card (with some help from TD).
The card contains 10 puzzles. By splitting the answers into pairs of digits, then drawing lines between the dots on the cover for each pair of digits (eg if an answer is 201304, draw a line from dot 20 to dot 13 and another line from dot 13 to dot 4), you will reveal a Christmas themed picture. Colouring any region containing an even number of unused dots green and colour any region containing an odd number of unused dots red or blue will make the picture even nicer.
If you're in the UK and want some copies of the card to send to your maths-loving friends, you can order them at mscroggs.co.uk/cards.
If you want to try the card yourself, you can download this printable A4 pdf. Alternatively, you can find the puzzles below and type the answers in the boxes. The answers will automatically be used to join the dots and the appropriate regions coloured in...
×10      ×9      ×4      ×5      ×5
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
I enjoyed solving problems for this card very much! Thanks a lot! I had a great time!
Happy New Year! Greetings from Ukraine.
Anna
                 Reply
Matt, great card this year! Problems 1 and 2 are slightly ambiguous though in that you did not specify that each digit could only be used once.

I initially thought the answers were simply 44×44 = 1936 and 99×99999999 = 9899999901, respectively ????
Dan Whitman
×1      ×1           Reply
I find that I can enter seven correct answers without issue. however, an eighth answer causes the entire tree to vanish.

I'm using Firefox on Windows 11.
hakon
                 Reply
@HJ: I can't reproduce that error on Firefox or Chrome on Ubuntu - although I did notice I'd left some debug outputting on, which I've now removed. Perhaps that was causing the issue.

If anyone else hits this issue, please let me know.
Matthew
            ×1     Reply
On my machine (Mac, using either Firefox or Chrome, including private mode so no plugins) the puzzle disappears when I complete the answers for 1, 3 and 9. I'm presuming my answers are correct -- the pattern they create is pretty clear and looks reasonable.
HJ
                 Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "k" then "i" then "t" then "e" in the box below (case sensitive):
 2023-12-08 
In November, I spent some time (with help from TD) designing this year's Chalkdust puzzle Christmas card.
The card looks boring at first glance, but contains 10 puzzles. By colouring in the answers to the puzzles on the front of the card in the colours given (each answer appears four time), you will reveal a Christmas themed picture.
If you're in the UK and want some copies of the card to send to your maths-loving friends, you can order them at mscroggs.co.uk/cards.
If you want to try the card yourself, you can download this printable A4 pdf. Alternatively, you can find the puzzles below and type the answers in the boxes. The answers will automatically be found and coloured in...
13 36 8 13 32 34 18 18 81 81 32 7 11 1 20 40 75 12 94 36 2 2 11 20 7 1 34 11 10 18 64 88 94 60 94 64 94 88 88 60 88 64 2 64 43 2 43 40 49 49 12 60 75 10 49 32 81 18 49 20 34 36 32 40 75 12 43 40 43 12 60 75 36 34 4 11 20 7 10 10 8 7 13 13 4 8 8 1 4 4 1 81
×21      ×15      ×7      ×8      ×13
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
Incorrect answers are treated is correct.

Looking at the JavaScript code, I found that any value that is a key in the array "regions" is treated as correct for all puzzles.
Lars Nordenström
×4   ×4   ×4   ×4   ×4     Reply
My visual abilities fail me - managed to solve the puzzles but cannot see what the picture shows
Gantonian
×4   ×4   ×4   ×4   ×4     Reply
@nochum: It can't, so the answer to that one probably isn't 88.
Matthew
×4   ×5   ×5   ×5   ×5     Reply
how can a dodecagon with an area of 88 fit inside anything with an area of 62.83~?
nochum
×4   ×4   ×4   ×4   ×2     Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "elbatnuocnu" backwards in the box below (case sensitive):
 2023-09-02 
This week, I've been at Talking Maths in Public (TMiP) in Newcastle. TMiP is a conference for anyone involved in—or interested in getting involved in—any sort of maths outreach, enrichment, or public engagement activity. It was really good, and I highly recommend coming to TMiP 2025.
The Saturday morning at TMiP was filled with a choice of activities, including a puzzle hunt written by me: the Tyne trial. At the start/end point of the Tyne trial, there was a locked box with a combination lock. In order to work out the combination for the lock, you needed to find some clues hidden around Newcastle and solve a few puzzles.
Every team taking part was given a copy of these instructions. Some people attended TMiP virtually, so I also made a version of the Tyne trial that included links to Google Street View and photos from which the necessary information could be obtained. You can have a go at this at mscroggs.co.uk/tyne-trial/remote. For anyone who wants to try the puzzles without searching through virtual Newcastle, the numbers that you needed to find are:
The solutions to the puzzles and the final puzzle are below. If you want to try the puzzles for yourself, do that now before reading on.

Puzzle for clue #2: Palindromes

We are going to start with a number then repeat the following process: if the number you have is a palindrome, stop; otherwise add the number to itself backwards. For example, if we start with 219, then we do: $$219\xrightarrow{+912}1131\xrightarrow{+1311}2442.$$ If you start with the number \(10b+9\) (ie 59), what palindrome do you get?
(If you start with 196, it is unknown whether you will ever get a palindrome.)

Show solution

Puzzle for clue #3: Mostly ones

There are 12 three-digit numbers whose digits are 1, 2, 3, 4, or 5 with exactly two digits that are ones. How many \(c\)-digit (ie 1838-digit) numbers are there whose digits are 1, 2, 3, 4, or 5 with exactly \(c-1\) digits (ie 1837) that are ones?

Show solution

Puzzle for clue #4: is it an integer?

The largest value of \(n\) such that \((n!-2)/(n-2)\) is an integer is 4. What is the largest value of \(n\) such that \((n!-d)/(n-d)\) (ie \((n!-1931)/(n-1931)\)) is an integer?

Show solution

Puzzle for clue #5: How many steps?

We are going to start with a number then repeat the following process: if we've reached 0, stop; otherwise subtract the smallest prime factor of the current number. For example, if we start with 9, then we do: $$9\xrightarrow{-3}6\xrightarrow{-2}4\xrightarrow{-2}2\xrightarrow{-2}0.$$ It took 4 steps to get to 0. What is the smallest starting number such that this process will take \(e\) (ie 1619) steps?

Show solution

Puzzle for clue #6: Four-digit number

I thought of a four digit number. I removed a digit to make a three digit number, then added my two numbers together. The result is \(200f+127\) (ie 9727). What was my original number?

Show solution

Puzzle for clue #7: Dice

If you roll two six-sided fair dice, the most likely total is 7. What is the most likely total if you rolled \(1470+g\) (ie 2470) dice?

Show solution

The final puzzle

The final puzzle involves using the answers to the five puzzles to find the four digit code that opens the box (and the physical locked box that was in the library on Saturday. To give hints to this code, each clue was given a "score".
The score of a number is the number of values of \(i\) such that the \(i\)th digit of the code is a factor of the \(i\)th digit of the number. For example, if the code was 1234, then the score of the number 3654 would be 3 (because 1 is a factor of 3; 2 is a factor of 6; and 4 is a factor of 4).
The seven clues to the final code are:

Show solution

×5      ×4      ×4      ×4      ×4
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "j" then "u" then "m" then "p" in the box below (case sensitive):
Image: Chalkdust Magazine

Chalkdust issue 17

 2023-05-22 
For the past couple of months, I've once again been spending an awful lot of my spare time working on Chalkdust. Today you can see the result of all this hard work: Chalkdust issue 17. I recommend checking out the entire magazine: you can read it online or order a physical copy.
My most popular contribution to the magazine is probably the crossnumber. I enjoyed writing this one; hope you enjoy solving it.
I also spent some time making this for the back page of the magazine. It's probably the most fun I've had making something stupid for Chalkdust for ages.
Chalkdust Magazine
×3      ×5      ×4      ×3      ×4
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "quotient" in the box below (case sensitive):
 2022-12-04 
In November, I spent some time (with help from TD) designing this year's Chalkdust puzzle Christmas card.
The card looks boring at first glance, but contains 11 puzzles. By colouring in the answers to the puzzles on the front of the card in black (each answer appears twice), then colouring remaining squares containing 0s red, and regions containing a star brown, you will reveal a Christmas themed picture.
If you want to try the card yourself, you can download this printable A4 pdf. Alternatively, you can find the puzzles below and type the answers in the boxes. The answers will automatically be found and coloured in black, and appropriate squares and regions will be coloured red and brown...
4 5 6 2 8 2 3 6 7 2 4 2 7 0 9 8 4 4 8 9 7 2 4 7 2 9 7 6 7 3 8 9 6 2 3 9 6 3 0 2 2 6 2 8 8 4 2 2 9 0 4 4 8 2 9 9 7 4 8 7 9 7 3 3 2 6 9 3 0 8 3 8 9 9 6 9 3 0 7 9 6 9 3 2 2 6 7 6 9 6 8 0 9 9 2 6 8 2 8 8 8 7 9 3 7 6 2 9 3 7 5 3 9 1 8 3 2 8 2 2 6 2 2 7 2 8 7 6 7 9 8 8 1 9 9 3 2 7 3 9 3 6 9 2 8 6 9 7 4 2 6 2 6 3 8 9 9 6 0 0 9 3 8 9 3 6 8 3 7 9 0 0 6 8 8 9 8
×2      ×2      ×1      ×2      ×2
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
@Nicki: If you're correct the picture should look suitably Christmassy
Matthew
   ×1              Reply
Where can I find out if I am correct?
Nicki
                 Reply
@Graeme Johnston: If you're right the picture should look suitably Christmassy
Matthew
                 Reply
Great fun thanks. At first they seem impossible but then a way through appears! How do I get the answers / check if I’m right?
Graeme Johnston
                 Reply
@Mike: The final picture doesn't have to be symmetric
Matthew
   ×2      ×1        Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "zero" in the box below (case sensitive):

Archive

Show me a random blog post
 2025 

Jan 2025

Christmas (2024) is over
Friendly squares
 2024 
▼ show ▼
 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

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2025