But meanwhile, I should show this post to my 8-year-old, who recently finished playing through a Kirby game and won’t stop talking about it. He might appreciate it, but perhaps in a
different way to me.
Why must a blog comment be text? Why could it not be… a drawing?1
I started hacking about and playing with a few ideas and now, on selected posts including this one, you can draw me a comment instead of typing one.
I opened the feature, experimentally (in a post available only to RSS subscribers2) the
other week, but now you get a go! Also, I’ve open-sourced the whole thing, in case you want to pick it apart.
What are you waiting for: scroll down, and draw me a comment!
Footnotes
1 I totally know the reasons that a blog comment shouldn’t be a drawing; I’m not
completely oblivious. Firstly, it’s less-expressive: words are versatile and you can do a lot with them. Secondly, it’s higher-bandwidth: images take up more space, take longer to
transmit, and that effect compounds when – like me – you’re tracking animation data too. But the single biggest reason, and I can’t stress this enough, is… the
penises. If you invite people to draw pictures on your blog, you’re gonna see a lot of penises. Short penises, long penises, fat penises, thin penises. Penises of every shape
and size. Some erect and some flacid. Some intact and some circumcised. Some with hairy balls and some shaved. Many of them urinating or ejaculating. Maybe even a few with smiley
faces. And short of some kind of image-categorisation AI thing, you can’t realistically run an anti-spam tool to detect hand-drawn penises.
2 I’ve copied a few of my favourites of their drawings below. Don’t forget to subscribe if you want early access to any weird shit I make.
I was browsing (BBC) Good Food today when I noticed something I’d not seen before: a “premium” recipe, available on their “app only”:
I clicked on the “premium” recipe and… it
looked just like any other recipe. I guess it’s not actually restricted after all?
Just out of curiosity, I fired up a more-vanilla web browser and tried to visit the same page. Now I saw an overlay and modal attempting1 to
restrict access to the content:
It turns out their entire effort to restrict access to their premium content… is implemented in client-side JavaScript. Even when I did see the overlay and not get access to
the recipe, all I needed to do was open my browser’s debugger and run document.body.classList.remove('tp-modal-open'); for(el of document.querySelectorAll('.tp-modal,
.tp-backdrop')) el.remove(); and all the restrictions were lifted.
What a complete joke.
Why didn’t I even have to write my JavaScript two-liner to get past the restriction in my primary browser? Because I’m running privacy-protector Ghostery, and one of the services Ghostery blocks by-default is one called Piano. Good Food uses Piano to segment their audience in your
browser, but they haven’t backed that by any, y’know, actual security so all of their content, “premium” or not, is available to anybody.
I’m guessing that Immediate Media (who bought the BBC Good Food brand a while back and have only just gotten around to stripping “BBC” out of
the name) have decided that an ad-supported model isn’t working and have decided to monetise the site a little differently2.
Unfortunately, their attempt to differentiate premium from regular content was sufficiently half-hearted that I barely noticed that, too, gliding through the paywall without
even noticing were it not for the fact that I wondered why there was a “premium” badge on some of their recipes.
Recipes probably aren’t considered a high-value target, of course. But I can tell you from experience that sometimes companies make basically this same mistake with much
more-sensitive systems. The other year, for example, I discovered (and ethically disclosed) a fault in the implementation of the login forms of a major UK mobile network that meant that
two-factor authentication could be bypassed entirely from the client-side.
These kinds of security mistakes are increasingly common on the Web as we train developers to think about the front-end first (and sometimes, exclusively). We need to do
better.
Footnotes
1 The fact that I could literally see the original content behind the modal
was a bit of a giveaway that they’d only hidden it, not actually protected it in any way.
2 I can see why they’d think that: personally, I didn’t even know there were ads
on the site until I did the experiment above: turns out I was already blocking them, too, along with any anti-ad-blocking scripts that might have been running alongside.
FoundryVTT is a fantastic Web-based environment for tabletop roleplaying adventures1 and something I
particularly enjoy is the freedom for virtually-unlimited scripting. Following a demonstration to a fellow DM at work last week I
promised to throw together a quick tutorial into scripting simple multi-phase maps using Foundry.2
Why multi-phase maps?
You might use a multi-phase map to:
Allow the development and expansion of a siege camp outside the fortress where the heroes are holed-up.3
Rotate through day and night cycles or different times of day, perhaps with different things to interact with in each.4
Gradually flood a sewer with rising water… increasing the range of the monster that dwells within.5
Re-arrange parts of the dungeon when the characters flip certain switches, opening new paths… and closing others.
I’ll use the map above to create a simple linear flow, powered by a macro in the hotbar. Obviously, more-complex scenarios are available, and combining this approach with a plugin like
Monk’s Active Tile Triggers can even be used to make the map appear to dynamically change in response to the movement
or actions of player characters!
Setting the scene
Create a scene, using the final state of the map as the background. Then, in reverse-order, add the previous states as tiles above it.
Make a note of the X-position that your tiles are in when they’re where they supposed to be: we’ll “move” the tiles off to the side when they’re hidden, to prevent their ghostly
half-hidden forms getting in your way as game master. We’ll also use this X-position to detect which tiles have already been moved/hidden.
Also make note of each tile’s ID, so your script can reference them. It’s easiest to do this as you go along. When you’re ready to write your macro, reverse the list, because
we’ll be hiding each tile in the opposite order from the order you placed them.
Writing the script
Next, create a new script macro, e.g. by clicking an empty slot in the macro bar. When you activate this script, the map will move forward one phase (or, if it’s at the end, it’ll
reset).
Here’s the code you’ll need – the 👈 emoji identifies the places you’ll need to modify the code, specifically:
const revealed_tiles_default_x = 250 should refer to the X-position of your tiles when they’re in the correct position.
const revealed_tiles_modified_x = 2825 should refer to the X-position they’ll appear at “off to the right” of your scene. To determine this, just move one tile right
until it’s sufficiently out of the way of the battlemap and then check what it’s X-position is! Or just take the default X-position, add the width of your map in pixels, and then add
a tiny bit more.
const revealed_tiles = [ ... ] is a list of the tile IDs of each tile what will be hidden, in turn. In my example there are five of them (the sixth and final image being
the scene background).
const revealed_tiles_default_x =250; // 👈 X-position of tiles when displayedconst revealed_tiles_modified_x =2825; // 👈 X-position of tiles when not displayedconst revealed_tiles = [
'2xG7S8Yqk4x1eAdr', // 👈 list of tile IDs in order that they should be hidden'SjNQDBImHvrjAHWX', // (top to bottom)'tuYg4FvLgIla1l21',
'auX4sj64PWmkAteR',
'yAL4YP0I4Cv4Sevt',
].map(t=>canvas.tiles.get(t));
/*************************************************************************************************/// Get the topmost tile that is still visible:const next_revealed_tile_to_move = revealed_tiles.find(t=>
t.position.x == revealed_tiles_default_x
);
// If there are NO still-visible tiles, we must need to reset the map:if( ! next_revealed_tile_to_move ) {
// To reset the map, we go through each tile and put it back where it belongs -for(tile of revealed_tiles){
canvas.scene.updateEmbeddedDocuments("Tile", [ {
_id: tile.id,
x: revealed_tiles_default_x,
hidden:false
} ]);
}
} else {
// Otherwise, hide the topmost visible tile (and move it off to the side to help the GM) -
canvas.scene.updateEmbeddedDocuments("Tile", [ {
_id: next_revealed_tile_to_move.id,
x: revealed_tiles_modified_x,
hidden:true
} ]);
}
I hope that the rest of the code is moderately self-explanatory for anybody with a little JavaScript experience, but if you’re just following this kind of simple, linear case then you
don’t need to modify it anyway. But to summarise, what it does is:
Finds the first listed tile that isn’t yet hidden (by comparing its X-position to the pre-set X-position).
If there aren’t any such tiles, we must have hidden them all already, so perform a reset: to do this – iterate through each tile and set its X-position to the pre-set X-position,
and un-hide it.
Otherwise, move the first not-hidden tile to the alternative X-position and hide it.
4 If you’re using Dungeon
Alchemist as part of your mapmaking process you can just export orthographic or perspective outputs with different times of day and your party’s regular inn can be
appropriately lit for any time of day, even if the party decides to just “wait at this table until nightfall”.
RotatingSandwiches.com is a website showcasing animated GIF files of rotating
sandwiches1. But it’s got a problem: 2 of the 51 sandwiches rotate the
wrong way. So I’ve fixed it:
My fix is available as a userscript on GreasyFork, so you can use your
favourite userscript manager2
to install it and the rotation will be fixed for you too. Here’s the code (it’s pretty simple):
1
2
3
4
5
6
7
8
9
10
11
12
// ==UserScript==// @name Standardise sandwich rotation on rotatingsandwiches.com// @namespace rotatingsandwiches.com.danq.me// @match https://rotatingsandwiches.com/*// @grant GM_addStyle// @version 1.0// @author Dan Q <https://danq.me/>// @license The Unlicense / Public Domain// @description Some sandwiches on rotatingsandwiches.com rotate in the opposite direction to the majority. 😡 Let's fix that.// ==/UserScript==
GM_addStyle('.q23-image-216, .q23-image-217 { transform: scaleX(-1); }');
Unless you’re especially agitated by irregular sandwich rotation, this is perhaps the most-pointless userscript ever created. So why did I go to the trouble?
Fixing Websites
Obviously, I’m telling you this as a vehicle to talk about userscripts in general and why you should be using them.
But the real magic is being able to remix the web your way. With just a little bit of CSS or JavaScript experience you
can stop complaining that a website’s design has changed in some way you don’t like or that some functionality you use isn’t as powerful or convenient as you’d like and you can fix
it.
A website I used disables scrolling until all their (tracking, advertising, etc.) JavaScript loads, and my privacy blocker blocks those files: I could cave and disable my browser’s
privacy tools… but it was almost as fast to add setInterval(()=>document.body.style.overflow='', 200); to a userscript and now it’s fixed.
Don’t want a Sports section on your BBC News homepage (not just the RSS
feed!)? document.querySelector('a[href="/sport"]').closest('main > div').remove(). Sorted.
I’m a huge fan of building your own tools to “scratch your own itch”. Userscripts are a highly accessible introduction to doing so that even beginner programmers can get on board with
and start getting value from. More-advanced scripts can do immensely clever and powerful things, but even if you just use them to apply a few light CSS touches to your favourite websites, that’s still a win.
Footnotes
1 Remember when a website’s domain name used to be connected to what it was for?
RotatingSandwiches.com does.
I’m testing a handful of highly-experimental new features on my personal website using multivariate (“A/B”) testing.
If you visit within the next day or so you’re likely to be randomly-selected to try out one of them. (If you’re not selected, you can manually enable one of the
experiments.)
I’d love to hear your feedback on these Very Serious New Features! Let me know which one(s) you see and whether you think they should become permanent fixtures on my site.
I was contacted this week by a geocacher called Dominik who, like me, loves geocaching…. but hates it when the coordinates for a cache are hidden behind a virtual jigsaw puzzle.
A popular online jigsaw tool used by lazy geocache owners is Jigidi: I’ve come up with severaltechniques for bypassing their puzzles or at least making
them easier.
I experimented with a few ways to work-around the jigsaw, e.g. dramatically increasing the “snap range” so dragging a piece any distance would result in it jumping to a
neighbour, and extracting original image URLs from localStorage. All were good, but none were
perfect.
Then I realised that – unlike Jigidi, where there can be a congratulatory “completion message” (with e.g. geocache coordinates in) – in JigsawExplorer the prize is seeing the
completed jigsaw.
Let’s work on attacking that bit of functionality. After all: if we can bypass the “added challenge” we’ll be able to see the finished jigsaw and, therefore, the geocache
coordinates. Like this:
Hackaround
Open a jigsaw and try the “box cover” button at the top. If you get the message “This puzzle’s box top preview is disabled for added challenge.”, carry on.
Open your browser’s debug tools (F12) and navigate to the Sources tab.
Find the jigex-prog.js file. Right-click and select Override Content (or Add Script Override).
In the overridden version of the file, search for the string – e&&e.customMystery?tt.msgbox("This puzzle's box top preview is disabled for added challenge."): –
this code checks if the puzzle has the “custom mystery” setting switched on and if so shows the message, otherwise (after the :) shows the box cover.
Carefully delete that entire string. It’ll probably appear twice.
Reload the page. Now the “box cover” button will work.
The moral, as always, might be: don’t put functionality into the client-side JavaScript if you don’t want the user to be able to bypass it.
Or maybe the moral is: if you’re going to make a puzzle geocache, put some work in and do something clever, original, and ideally with fieldwork rather than yet another low-effort
“upload a picture and choose the highest number of jigsaw pieces to cut it into from the dropdown”.
Progressive enhancement is a great philosophy for Web application development. Deliver all the essential basic functionality using the simplest standards available; use advanced
technologies to add bonus value and convenience features for users whose platform supports them. Win.
In Three Rings, for example, volunteers can see a “starchart” of the volunteering shifts they’ve done recently, at-a-glance, on
their profile page1.
In the most basic case, this is usable in its HTML-only form: even with no JavaScript, no CSS, no images even, it still functions. But if JavaScript is enabled, the volunteer can dynamically “filter” the year(s) of volunteering
they’re viewing. Basic progressive enhancement.
If a feature requires JavaScript, my usual approach is to use JavaScript to add the relevant user interface to the page in the first place. Those starchart filters in Three
Rings don’t appear at all if JavaScript is disabled. A downside to this approach is that the JavaScript necessarily modifies the DOM on page load, which introduces a delay to the page being interactive as well as potentially resulting in layout shift.
That’s not always the best approach. I was reminded of this today by the website of 7-year-old Shiro (produced with, one assumes, at least
a little help from Saneef H. Ansari). Take a look at this progressively-enhanced theme switcher:
The HTML that’s delivered over-the-wire provides a disabled<select> element, which gains the CSS directive cursor: not-allowed;, to make it clear to the used that this dropdown doesn’t do anything. The whole thing’s wrapped
in a custom element.
When that custom element is defined by the JavaScript, it enhances the dropdown with an event listener that implements the theme changes, then enables the disabled
<select>.
It’s probably no inconvenience to the minority of JS-less users to see a theme switcher than, when they go to use it, turns out to be
disabled. But it saves time for virtually everybody not to have to wait for JavaScript to manipulate the DOM, or else to risk
shifting the layout by revealing a previously-hidden element.
Altogether, this is a really clever approach, and I was pleased today to be reminded – by a 7-year-old! – of the elegance of this approach. Nice one Shiro (and Saneef!).
Footnotes
1 Assuming that administrators at the organisation where they volunteer enable this
feature for them, of course: Three Rings‘ permission model is robust and highly-customisable. Okay, that’s enough sales pitch.
A year and a half ago I came up with a technique for intercepting the “shuffle” operation
on jigsaw website Jigidi, allowing players to force the pieces to appear in a consecutive “stack” for ludicrously easy solving. I did this
partially because I was annoyed that a collection of geocaches near me used Jigidi puzzles as a barrier to their coordinates1…
but also because I enjoy hacking my way around artificially-imposed constraints on the Web (see, for example, my efforts last week to circumvent region-blocking on radio.garden).
My solver didn’t work for long: code changes at Jigidi’s end first made it harder, then made it impossible, to use the approach I suggested. That’s fine by me – I’d already got what I
wanted – but the comments thread on that post suggests that there’s
a lot of people who wish it still worked!2
And so I ignored the pleas of people who wanted me to re-develop a “Jigidi solver”. Until recently, when I once again needed to solve a jigsaw puzzle in order to find a geocache’s
coordinates.
Making A Jigidi Helper
Rather than interfere with the code provided by Jigidi, I decided to take a more-abstract approach: swapping out the jigsaw’s image for one that would be easier.
This approach benefits from (a) having multiple mechanisms of application: query interception, DNS hijacking, etc., meaning that if one stops working then another one can be easily
rolled-out, and (b) not relying so-heavily on the structure of Jigidi’s code (and therefore not being likely to “break” as a result of future upgrades to Jigidi’s platform).
It’s not as powerful as my previous technique – more a “helper” than a “solver” – but it’s good enough to shave at least half the time off that I’d otherwise spend solving a Jigidi
jigsaw, which means I get to spend more time out in the rain looking for lost tupperware. (If only geocaching were even the weirdest of my hobbies…)
How To Use The Jigidi Helper
To do this yourself and simplify your efforts to solve those annoying “all one colour” or otherwise super-frustrating jigsaw puzzles, here’s what you do:
Visit a Jigidi jigsaw. Do not be logged-in to a Jigidi account.
Open your browser’s debug tools (usually F12). In the Console tab, paste it and press enter. You can close your debug tools again (F12) if you like.
Press Jigidi’s “restart” button, next to the timer. The jigsaw will restart, but the picture will be replaced with one that’s easier-to-solve than most, as described below.
Once you solve the jigsaw, the image will revert to normal (turn your screen around and show off your success to a friend!).
What makes it easier to solve?
The replacement image has the following characteristics that make it easier to solve than it might otherwise be:
Every piece has written on it the row and column it belongs in.
Every “column” is striped in a different colour.
Striped “bands” run along entire rows and columns.
To solve the jigsaw, start by grouping colours together, then start combining those that belong in the same column (based on the second digit on the piece). Join whole or partial
columns together as you go.
I’ve been using this technique or related ones for over six months now and no code changes on Jigidi’s side have impacted upon it at all, so it’s probably got better longevity than the
previous approach. I’m not entirely happy with it, and you might not be either, so feel free to fork my code and improve it: the legiblity of the numbers is sometimes suboptimal, and
the colour banding repeats on larger jigsaws which I’d rather avoid. There’s probably also potential to improve colour-recognition by making the colour bands span the gaps
between rows or columns of pieces, too, but more experiments are needed and, frankly, I’m not the right person for the job. For the second time, I’m going to abandon a tool
that streamlines Jigidi solving because I’ve already gotten what I needed out of it, and I’ll leave it up to you if you want to come up with an improvement and share it with the
community.
Footnotes
1 As I’ve mentioned before, and still nobody believes me: I’m not a fan of jigsaws! If you
enjoy them, that’s great: grab a bucket of popcorn and a jigsaw and go wild… but don’t feel compelled to share either with me.
2 The comments also include asuper-helpful person called Rich who’s been manually
solving people’s puzzles for them, and somebody called Perdita
who “could be my grandmother” (except: no) with whom I enjoyed a
conversation on- and off-line about the ethics of my technique. It’s one of the most-popular comment threads my blog has ever seen.
I’m off work sick today: it’s just a cold, but it’s had a damn good go at wrecking my lungs and I feel pretty lousy. You know how when you’ve got too much of a brain-fog to trust
yourself with production systems but you still want to write code (or is that just me?), so this morning I threw together a really,
really stupid project which you can play online here.
It’s inspired by a toot by Mason”Tailsteak” Williams (whom I’ve mentioned before once or
twice). At first I thought I’d try to calculate the odds of winning at his proposed game, or how many times one might expect to play before winning,
but I haven’t the brainpower for that in my snot-addled brain. So instead I threw together a terrible, terrible digital implementation.
Go play it if, like me, you’ve got nothing smarter that your brain can be doing today.
Finally got around to implementing a super-lightweight (~20 lines of code, 1 dependency) #spring83 key generator. There are plenty of others; nobody needs this one, but it’s free if you
want it:
I swear that I used to be good at Mastermind when I was a kid. But now, when it’s my turn to break
the code that one of our kids has chosen, I fail more often than I succeed. That’s no good!
Mastermind and me
Maybe it’s because I’m distracted; multitasking doesn’t help problem-solving. Or it’s because we’re “Super” Mastermind, which differs from the one I had as a child in that
eight (not six) peg colours are available and secret codes are permitted to have duplicate peg colours. These changes increase the possible permutations from 360 to 4,096, but the
number of guesses allowed only goes up from 8 to 10. That’s hard.
Hey, that’s an idea. Let’s crack the code… by writing some code!
Representing a search space
The search space for Super Mastermind isn’t enormous, and it lends itself to some highly-efficient computerised storage.
There are 8 different colours of peg. We can express these colours as a number between 0 and 7, in three bits of binary, like this:
Decimal
Binary
Colour
0
000
Red
1
001
Orange
2
010
Yellow
3
011
Green
4
100
Blue
5
101
Pink
6
110
Purple
7
111
White
There are four pegs in a row, so we can express any given combination of coloured pegs as a 12-bit binary number. E.g. 100 110 111 010 would represent the
permutation blue (100), purple (110), white (111), yellow (010). The total search space, therefore, is the range of numbers from
000000000000 through 111111111111… that is: decimal 0 through 4,095:
Decimal
Binary
Colours
0
000000000000
Red, red, red, red
1
000000000001
Red, red, red, orange
2
000000000010
Red, red, red, yellow
…………
4092
111111111100
White, white, white, blue
4093
111111111101
White, white, white, pink
4094
111111111110
White, white, white, purple
4095
111111111111
White, white, white, white
Whenever we make a guess, we get feedback in the form of two variables: each peg that is in the right place is a bull; each that represents a peg in the secret code but
isn’t in the right place is a cow (the names come from Mastermind’s precursor, Bulls & Cows). Four bulls
would be an immediate win (lucky!), any other combination of bulls and cows is still valuable information. Even a zero-score guess is valuable- potentially very valuable! – because it
tells the player that none of the pegs they’ve guessed appear in the secret code.
Solving with Javascript
The latest versions of Javascript support binary literals and bitwise operations, so we can encode and decode between arrays of four coloured pegs (numbers 0-7) and the number 0-4,095
representing the guess as shown below. Decoding uses an AND bitmask to filter to the requisite digits then divides by the order of magnitude. Encoding is just a reduce
function that bitshift-concatenates the numbers together.
/** * Decode a candidate into four peg values by using binary bitwise operations. */function decodeCandidate(candidate){
return [
(candidate &0b111000000000) /0b001000000000,
(candidate &0b000111000000) /0b000001000000,
(candidate &0b000000111000) /0b000000001000,
(candidate &0b000000000111) /0b000000000001
];
}
/** * Given an array of four integers (0-7) to represent the pegs, in order, returns a single-number * candidate representation. */function encodeCandidate(pegs) {
return pegs.reduce((a, b)=>(a <<3) + b);
}
With this, we can simply:
Produce a list of candidate solutions (an array containing numbers 0 through 4,095).
Choose one candidate, use it as a guess, and ask the code-maker how it scores.
Eliminate from the candidate solutions list all solutions that would not score the same number of bulls and cows for the guess that was made.
Repeat from step #2 until you win.
Step 3’s the most important one there. Given a function getScore( solution, guess ) which returns an array of [ bulls, cows ] a given guess would
score if faced with a specific solution, that code would look like this (I’m convined there must be a more-performant way to eliminate candidates from the list with XOR
bitmasks, but I haven’t worked out what it is yet):
/** * Given a guess (array of four integers from 0-7 to represent the pegs, in order) and the number * of bulls (number of pegs in the guess that are in the right place) and cows (number of pegs in the * guess that are correct but in the wrong place), eliminates from the candidates array all guesses * invalidated by this result. Return true if successful, false otherwise. */function eliminateCandidates(guess, bulls, cows){
const newCandidatesList = data.candidates.filter(candidate=>{
const score = getScore(candidate, guess);
return (score[0] == bulls) && (score[1] == cows);
});
if(newCandidatesList.length ==0) {
alert('That response would reduce the candidate list to zero.');
returnfalse;
}
data.candidates = newCandidatesList;
chooseNextGuess();
returntrue;
}
I continued in this fashion to write a full solution (source code). It uses ReefJS for
component rendering and state management, and you can try it for yourself right in your web browser. If you play against the online version I mentioned you’ll need to transpose the colours in your head: the physical version I play with the kids has pink and
purple pegs, but the online one replaces these with brown and black.
Testing the solution
Let’s try it out against the online version:
As expected, my code works well-enough to win the game every time I’ve tried, both against computerised and in-person opponents. So – unless you’ve been actively thinking about the
specifics of the algorithm I’ve employed – it might surprise you to discover that… my solution is very-much a suboptimal one!
My solution is suboptimal
A couple of games in, the suboptimality of my solution became pretty visible. Sure, it still won every game, but it was a blunt instrument, and anybody who’s seriously thought about
games like this can tell you why. You know how when you play e.g. Wordle (but not in “hard mode”) you sometimes want to type in a word that can’t possibly be the
solution because it’s the best way to rule in (or out) certain key letters? This kind of strategic search space bisection reduces the mean number of guesses you need to solve the
puzzle, and the same’s true in Mastermind. But because my solver will only propose guesses from the list of candidate solutions, it can’t make this kind of improvement.
Search space bisection is also used in my adverserial hangman game, but in this case the aim is to split the search space in such a way that no
matter what guess a player makes, they always find themselves in the larger remaining portion of the search space, to maximise the number of guesses they have to make. Y’know, because
it’s evil.
There are mathematically-derived heuristics to optimise Mastermind strategy. The first
of these came from none other than Donald Knuth (legend of computer science, mathematics, and pipe organs) back in 1977. His solution,
published at probably the height of the game’s popularity in the amazingly-named Journal of Recreational Mathematics, guarantees a solution to the six-colour version of the
game within five guesses. Ville [2013] solved an
optimal solution for a seven-colour variant, but demonstrated how rapidly the tree of possible moves grows and the need for early pruning – even with powerful modern computers – to
conserve memory. It’s a very enjoyable and readable paper.
But for my purposes, it’s unnecessary. My solver routinely wins within six, maybe seven guesses, and by nonchalantly glancing at my phone in-between my guesses I can now reliably guess
our children’s codes quickly and easily. In the end, that’s what this was all about.