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 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
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My visual abilities fail me - managed to solve the puzzles but cannot see what the picture shows
Gantonian
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@nochum: It can't, so the answer to that one probably isn't 88.
Matthew
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how can a dodecagon with an area of 88 fit inside anything with an area of 62.83~?
nochum
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 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.)

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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?

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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?

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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?

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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?

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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?

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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

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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
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 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
                        
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@Nicki: If you're correct the picture should look suitably Christmassy
Matthew
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Where can I find out if I am correct?
Nicki
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@Graeme Johnston: If you're right the picture should look suitably Christmassy
Matthew
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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
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@Mike: The final picture doesn't have to be symmetric
Matthew
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 2022-02-26 
Surprisingly often, people ask me how they can build their own copy of MENACE. If you've been thinking that you'd love your own matchbox-powered machine learning computer but haven't got round to asking me about it yet, then this blog post is just what you're looking for.

Matchboxes

Before building MENACE, you'll need to get hold of 304 matchboxes (plus a few spares in case one gets lost or falls apart). I used these craft matchboxes: they don't have the best build quality, but they're good enough.

304 positions

The positions you need to glue onto the front of the matchboxes can be downloaded from this GitHub repository (first move boxes, third move boxes, fifth move boxes, seventh move boxes). These are sized to fit on matchboxes that have 15mm by 35mm fronts.
I printed each pdf on differently coloured paper to make it easier to sort the matchboxes after getting them out of their box.
If you get differently sized matchboxes, the code used the generate the PDFs is in the same GitHub repository (you'll need to modify these lines). Alternatively, feel free to drop me an email and I will happily adjust the sizes for you and send you the updated PDFs.

Glue

I used PVA glue to stick the positions onto the matchboxes. The printable PDFs have extra tabs of paper above and below the postions that can be glued in to the bottom and inside of the matchbox tray to hold it more securely.
Gluing the positions onto the matchboxes was the most time consuming part of building my copy of MENACE, largely due to having to wait for the glue to dry on a set of matchboxes before I had space for the next batch of them to dry.

Beads

Once you've glued pictures of noughts and crosses positions to 304 matchboxes, you'll need to put coloured beads into each matchbox. For this, I used a large tub of Hama beads (that tub contained orders of magnitude more beads than I needed).
A nice side effect of using Hama beads is that they're designed to be ironed together so making a key to show which colour corresponds to each position is very easy.
I typically start the boxes off with 8 beads of each colour in the first move box, 4 of each colour in the third move boxes, 2 of each in the fifth move boxes, and one of each in the seventh move boxes.

Once you've filled all your matchboxes with the correct number of beads, you're ready to play yout first game against MENACE. I'd love to hear how you get on.
And once you're bored of playing noughts and crosses against your matchboxes, why not build a machine that learns to play Hexapawn, Connect 4, Chess or Go? Or one that plays Nim?
Edit: Added link to the printable pdfs of the positions needed for Hexapawn, made by Dan Whitman.
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Interesting.
Could try a same kind of thing using playing card deck(s)? A(=1)-2-3 4-5-6 7-8-9 maybe 3 decks with different colours on their backs.
Willem
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this if great!
Djonwaw
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I also read the Martin Gardner article way back when and had two matchbox machines (actually with envelopes instead of matchboxes) play Nim against each other. I don't remember all the details now, except that it got to the point where one would make the first move and the other would immediately resign.
Tim Lewis
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I made a matchbox machine that learns to play 3x3 Nim almost 50 years ago. I still have it. (Based on Martin Gardner's article)
Tony
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