## Woodward Draw

• Explore the set of 4 letter words
• Either change one letter of the previous word
• Or rearrange all the letters of the previous word
• Find all 105 picture words!

Woodward Draw by Daniel Linssen is the kind of game that my inner Scrabble player both loves and hates. I’ve been playing on and off for the last three days to complete it, and it’s been great. While not perfectly polished1 and with a few rough edges2, it’s still a great example of what one developer can do with a little time.

It deserves a hat tip of respect, but I hope you’ll give it more than that by going and playing it (it’s free, and you can play online or download a copy3). I should probably check out their other games!

## Footnotes

1 At one point the background colour, in order to match a picture word, changed to almost the same colour as the text of the three words to find!

2 The tutorial-like beginning is a bit confusing until you realise that you have to play the turn you’re told to, to begin with, for example.

## The Miracle Sudoku

I first saw this video when it was doing the rounds three years ago and was blown away. I was reminded of it recently when it appeared in a blog post about AI’s possible future role in research by Terence Eden.

I don’t even like sudoku. And if you’d told me in advance that I’d enjoy watching a man slowly solve a sudoku-based puzzle in real-time, I’d have called you crazy. But I watched it again today, for what must’ve been the third time, and it’s still magical. The artistry of puzzle creator Mitchell Lee is staggering.

If you somehow missed it the first time around, now’s your chance. Put this 25-minute video on in the background and prepare to have your mind blown.

## Solving Jigidi… Again

(Just want the instructions? Scroll down.)

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).

Watch a video demonstrating the approach:

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:

1. Visit a Jigidi jigsaw. Do not be logged-in to a Jigidi account.
2. Copy my JavaScript code into your clipboard.
3. 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.
4. 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.
5. 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.

## STAR T/W R/A E/R K/S

Fun little trick in the Sunday New York Times crossword yesterday: the central theme clue was “The better of two sci-fi franchises”, and regardless of whether you put Star Wars or Star Trek, the crossing clues worked

This is a (snippet of an) excellent New York Times crossword puzzle, but the true genius of it in my mind is that 71 down can be answered using iconic Star Wars line “It’s a trap!” only if the player puts Star Trek, rather than Star Wars, as the answer to 70 across (“The better of two sci-fi franchises”). If they answer with Star Wars, they instead must answer “It’s a wrap!”.

Matt goes on to try to make his own which pairs 1954 novel Lord of the Rings against Lord of the Flies, which is pretty good but I’m not convinced he can get away with the crosswise “ulne” as a word (contrast e.g. “rise” in the example above).

Of course, neither are quite as clever as the New York Timespuzzle on the eve of the 1996 presidential election whose clue “Lead story in tomorrow’s newspaper(!)” could be answered either “Clinton elected” or “Bob Dole elected” and the words crossing each of “Clinton” or “Bob Dole” would still fit the clues (despite being modified by only a single letter).

If you’re looking to lose some time, here’s some further reading on so-called “Schrödinger puzzles”, and several  more crosswords that achieve the same feat.

×

## Tick Tock

Looking for something with an “escape room” vibe for our date night this week, Ruth and I tried Tick Tock: A Tale for Two, a multiplayer simultaneous cooperative play game for two people, produced by Other Tales Interactive. It was amazing and I’d highly recommend it.

The game’s available on a variety of platforms: Windows, Mac, Android, iOS, and Nintendo Switch. We opted for the Android version because, thanks to Google Play Family Library, this meant we only had to buy one copy  (you need it installed on both devices you’re playing it on, although both devices don’t have to be of the same type: you could use an iPhone and a Nintendo Switch for example).

The really clever bit from a technical perspective is that the two devices don’t communicate with one another. You could put your devices in flight mode and this game would still work just fine! Instead, the gameplay functions by, at any given time, giving you either (a) a puzzle for which the other person’s device will provide the solution, or (b) a puzzle that you both share, but for which each device only gives you half of the clues you need. By working as a team and communicating effectively (think Keep Talking and Nobody Explodes but without the time pressure), you and your partner will solve the puzzles and progress the plot.

(We’re purists for this kind of puzzle game so we didn’t look at one another’s screens, but I can see how it’d be tempting to “cheat” in this way, especially given that even the guys in the trailer do so!)

The puzzles start easy enough, to the extent that we were worried that the entire experience might not be challenging for us. But the second of the three acts proved us wrong and we had to step up our communication and coordination, and the final act had one puzzle that had us scratching our heads for some time! Quite an enjoyable difficulty curve, but still balanced to make sure that we got to a solution, together, in the end. That’s a hard thing to achieve in a game, and deserves praise.

The plot is a little abstract at times and it’s hard to work out exactly what role we, the protagonists, play until right at the end. That’s a bit of a shame, but not in itself a reason to reject this wonderful gem of a game. We spent 72 minutes playing it, although that includes a break in the middle to eat a delivery curry.

If you’re looking for something a bit different for a quiet night in with somebody special, it’s well worth a look.

× × × ×

## Quickly Solving Jigidi Puzzles

tl;dr? Just want instructions on how to solve Jigidi puzzles really fast with the help of your browser’s dev tools? Skip to that bit.

This approach doesn’t work any more. Want to see one that still does (but isn’t quite so automated)? Here you go!

## I don’t enjoy jigsaw puzzles

I enjoy geocaching. I don’t enjoy jigsaw puzzles. So mystery caches that require you to solve an online jigsaw puzzle in order to get the coordinates really don’t do it for me. When I’m geocaching I want to be outdoors exploring, not sitting at my computer gradually dragging pixels around!

Many of these mystery caches use Jigidi to host these jigsaw puzzles. An earlier version of Jigidi was auto-solvable with a userscript, but the service has continued to be developed and evolve and the current version works quite hard to make it hard for simple scripts to solve. For example, it uses a WebSocket connection to telegraph back to the server how pieces are moved around and connected to one another and the server only releases the secret “you’ve solved it” message after it detects that the pieces have been arranged in the appropriate relative configuration.

If there’s one thing I enjoy more than jigsaw puzzles – and as previously established there are about a billion things I enjoy more than jigsaw puzzles – it’s reverse-engineering a computer system to exploit its weaknesses. So I took a dive into Jigidi’s client-side source code. Here’s what it does:

1. Get from the server the completed image and the dimensions (number of pieces).
2. Cut the image up into the appropriate number of pieces.
3. Shuffle the pieces.
4. Establish a WebSocket connection to keep the server up-to-date with the relative position of the pieces.
5. Start the game: the player can drag-and-drop pieces and if two adjacent pieces can be connected they lock together. Both pieces have to be mostly-visible (not buried under other pieces), presumably to prevent players from just making a stack and then holding a piece against each edge of it to “fish” for its adjacent partners.

Looking at that process, there’s an obvious weak point – the shuffling (point 3) happens client-side, and before the WebSocket sync begins. We could override the shuffling function to lay the pieces out in a grid, but we’d still have to click each of them in turn to trigger the connection. Or we could skip the shuffling entirely and just leave the pieces in their default positions.

And what are the default positions? It’s a stack with the bottom-right jigsaw piece on the top, the piece to the left of it below it, then the piece to the left of that and son on through the first row… then the rightmost piece from the second-to-bottom row, then the piece to the left of that, and so on.

That’s… a pretty convenient order if you want to solve a jigsaw. All you have to do is drag the top piece to the right to join it to the piece below that. Then move those two to the right to join to the piece below them. And so on through the bottom row before moving back – like a typewriter’s carriage return – to collect the second-to-bottom row and so on.

## How can I do this?

If you’d like to cheat at Jigidi jigsaws, this approach works as of the time of writing. I used Firefox, but the same basic approach should work with virtually any modern desktop web browser.

2. Pop up your browser’s developer tools (F12, usually) and switch to the Debugger tab. Open the file `game/js/release.js` and uncompress it by pressing the {} button, if necessary.
3. Find the line where the code considers shuffling; right now for me it’s like 3671 and looks like this:
`return this.j ? (V.info('board-data-bytes already exists, no need to send SHUFFLE'), Promise.resolve(this.j)) : new Promise(function (d, e) {`
4. Set a breakpoint on that line by clicking its line number.
5. Restart the puzzle by clicking the restart button to the right of the timer. The puzzle will reload but then stop with a “Paused on breakpoint” message. At this point the application is considering whether or not to shuffle the pieces, which normally depends on whether you’ve started the puzzle for the first time or you’re continuing a saved puzzle from where you left off.
6. In the developer tools, switch to the Console tab.
7. Type: `this.j = true` (this ensures that the ternary operation we set the breakpoint on will resolve to the true condition, i.e. not shuffle the pieces).
8. Press the play button to continue running the code from the breakpoint. You can now close the developer tools if you like.
9. Solve the puzzle as described/shown above, by moving the top piece on the stack slightly to the right, repeatedly, and then down and left at the end of each full row.

Update 2021-09-22: Abraxas observes that Jigidi have changed their code, possibly in response to this shortcut. Unfortunately for them, while they continue to perform shuffling on the client-side they’ll always be vulnerable to this kind of simple exploit. Their new code seems to be named not `release.js` but given a version number; right now it’s `14.3.1977`. You can still expand it in the same way, and find the shuffling code: right now for me this starts on line 1129:

Put a breakpoint on line 1129. This code gets called twice, so the first time the breakpoint gets hit just hit continue and play on until the second time. The second time it gets hit, move the breakpoint to line 1130 and press continue. Then use the console to enter the code `d = a.G` and continue. Only one piece of jigsaw will be shuffled; the rest will be arranged in a neat stack like before (I’m sure you can work out where the one piece goes when you get to it).

Update 2023-03-09: I’ve not had time nor inclination to re-“break” Jigidi’s shuffler, but on the rare ocassions I’ve needed to solve a Jigidi, I’ve come up with a technique that replaces a jigsaw’s pieces with ones that each show the row and column number they belong to, as well as colour-coding the rows and columns and drawing horizontal and vertical bars to help visual alignment. It makes the process significantly less-painful. It’s still pretty buggy code though and I end up tweaking it each and every time I use it, but it certainly works and makes jigsaws that lack clear visual markers (e.g. large areas the same colour) a lot easier.

× × × ×

## Break Into . Us (lock puzzle game)

I’ve made a puzzle game about breaking open padlocks. If you just want to play the game, go play the game. Or read on for the how-and-why of its creation.

About three months ago, my friend Claire, in a WhatsApp group we both frequent, shared a brainteaser:

The puzzle was to be interpreted as follows: you have a three-digit combination lock with numbers 0-9; so 1,000 possible combinations in total. Bulls and Cows-style, a series of clues indicate how “close” each of several pre-established “guesses” are. In “bulls and cows” nomenclature, a “bull” is a correctly-guessed digit in the correct location and a “cow” is a correctly-guessed digit in the wrong location, so the puzzle’s clues are:

• 682 – one bull
• 614 – one cow
• 206 – two cows
• 738 – no bulls, no cows
• 380 – one cow

By the time I’d solved her puzzle the conventional way I was already interested in the possibility of implementing a general-case computerised solver for this kind of puzzle, so I did. My solver uses a simple “brute force” technique, as follows:

1. Put all possible combinations into a search space.
2. For each clue, remove from the search space all invalid combinations.
3. Whatever combination is left is the correct answer.

Visualising the solver as a series of bisections of a search space got me thinking about something else: wouldn’t this be a perfectly reasonable way to programatically generate puzzles of this type, too? Something like this:

1. Put all possible combinations into a search space.
2. Randomly generate a clue such that the search space is bisected (within given parameters to ensure that neither too many nor too few clues are needed)
3. Repeat until only one combination is left

Interestingly, this approach is almost the opposite of what a human would probably do. A human, tasked with creating a puzzle of this sort, would probably choose the answer first and then come up with clues that describe it. Instead, though, my solution would come up with clues, apply them, and then see what’s left-over at the end.

I expanded my generator to go beyond simple bulls-or-cows clues: it’s also capable of generating clues that make reference to the balance of odd and even digits (in a numeric lock), the number of different digits used in the combination, the sum of the digits of the combination, and whether or not the correct combination “ascends” or “descends”. I’ve ideas for other possible clue types too, which could be valuable to make even tougher combination locks: e.g. specifying how many numbers in the combination are adjacent to a consecutive number, specifying the types of number that the sum of the digits adds to (e.g. “the sum of the digits is a prime number”) and so on.

Next up, I wanted to make a based interface so that people could have a go at the puzzles in their web browser, track their progress through the levels, get a “score” based on the number and difficulty of the locks that they’d cracked (so they can compare it to their friends), and save their progress to carry on next time.

I implemented in pure vanilla HTML, CSS, SVG and JS, with no dependencies. Compressed, it delivers to your browser and is ready-to-play in a little under 10kB, most of which is the puzzles themselves (which are pregenerated and stored in a JSON file). Naturally, it lends itself well to running offline, so it’s PWA-enhanced with a service worker so it can be “installed” onto your device, too, and it’ll check for bonus puzzles and other updates periodically.

Honestly, the hardest bit of implementing the frontend was the “spinnable” digits: depending on your browser, these are an endless-scrolling <ul> implemented mostly in CSS and with snap points set, and then some JS to work out “what you meant” based on where you span to. Which feels like the right way to implement such a thing, but was a lot more work than putting together my own control, not least because of browser inconsistencies in the implementation of snap points.

Anyway: you should go and play the game, now, and let me know what you think. Is it worth expanding and improving? Should I leave it as it is? I’m open to ideas (and if you don’t like that I’m not implementing your suggestions, you can always fork a copy of the code and change it yourself)!

Or if you’d like to see some of the other JavaScript experiments I’ve done, you might enjoy my “cheating” hangman game, my recreation of the lunar lander game I wrote in college, or rediscover that time I was ill and came up the worst conceivable tool to calculate Pi.

× × × × ×

## Who finished second?

Three athletes (and only three athletes) participate in a series of track and field events. Points are awarded for 1st, 2nd, and 3rd place in each event (the same points for each event, i.e. 1st always gets “x” points, 2nd always gets “y” points, 3rd always gets “z” points), with x > y > z > 0, and all point values being integers.
The athletes are named: Adam, Bob, and Charlie.

• Adam finished first overall with 22 points.
• Bob won the Javelin event and finished with 9 points overall.
• Charlie also finished with 9 points overall.

Question: Who finished second in the 100-meter dash (and why)?

I enjoyed this puzzle so much that I shared it with (and discussed it at length with) my smartypants puzzle-sharing group. Now it’s your turn. The answer, plus a full explanation, can be found on the other side of the link, but I’d recommend that you try to solve it yourself first. If it seems impossible at first glance, start by breaking it down into what you can know, and what you can almost know, and work from there. Good luck!

And if anybody feels like hiring Nick to come and speak anywhere near where I am, that’d be awesome of you.

## Elf Chalkboard Puzzle

I write the integers 1-9999 (inclusive) on a huge chalkboard. Each number is written once.

During the night the board is visited by a series of naughty math elves (it’s a thing!)

Each elf approaches the board, selects two numbers at random, erases them, and replaces them with a new number that is the absolute difference of the two numbers erased.

This vandalism continues all night until there is just one number remaining.

I return to the board the next morning and find the single number of the board. The question is: Is this remaining number odd or even?

A fun, lightweight maths puzzle for your amusement. I was able to find the right answer pretty quickly by spotting the pattern; it took me longer to find the words to adequately explain the pattern.

It’s likely that the first word ladder puzzles were created by none other than Lewis Carroll (Charles Lutwidge Dodgson), the talented British mathematician, and author of the Alice’s adventures. According to Carroll, he invented them on Christmas Day in 1877.

A word ladder puzzle consists of two end-cap words, and the goal is to derive a series of chain words that change one word to the other. At each stage, adjacent words on the ladder differ by the substitution of just one letter. Each chain word (or rung of the word ladder), also needs to be a valid word. Below is an example of turning TABLE into CROWN (this time, in nine steps):

TABLE → CABLE → CARLE → CARLS → CARPS → CORPS → COOPS → CROPS → CROWS → CROWN

In another example, it take four steps to turn WARM into COLD.

WARM → WARD → CARD → CORD → COLD

(As each letter of the two words in the last example is different, this is the minimum possible number of moves; each move changes one of the letters).

Nice one! Nick Berry does something I’ve often considered doing but never found the time by “solving” word ladders and finding longer chains than might have ever been identified before.

## Puzzle Montage Art by Tim Klein

Jigsaw puzzle companies tend to use the same cut patterns for multiple puzzles. This makes the pieces interchangeable, and I sometimes find that I can combine portions from two or more puzzles to make a surreal picture that the publisher never imagined. I take great pleasure in “discovering” such bizarre images lying latent, sometimes for decades, within the pieces of ordinary mass-produced puzzles.

## Mystery Pipe

A puzzle that the steam locomotive enthusiasts among you (you’re out there, right?) might stand a chance at solving:

The picture below is of “6040”, the last steam locomotive to be built for the Department of Railways New South Wales in Australia. She was in service as a coal/goods transporter from 1957 through 1967 before the increase in the use of diesel on the railways lead to the death of steam. She was eventually rescued and displayed by the New South Wales Railway Museum, which is where the photo was taken. There, starting from her 50th birthday, a team of volunteers have been restoring her. But that’s perhaps not the thing that’s most-unusual about her, or her class (AD60).

I’ve highlighted on the photo a feature that you’ve probably never seen before, even if you’re of an inclination to go “Ooh, a steam loco: I’mma have a closer look at that!”. What you’re seeing is an open pipe (with a funnel-like protrusion at one end) connecting the area behind the leading wheels to the cab. What’s it for? Have a think about it as you read the rest of this post, and see if you can come up with the answer before I tell you the answer.

These pipes weren’t initially fitted to “6040” nor to any of her 41 sisters: they were added later, once the need for them became apparent.

If you’re thinking “ventilation”, you’d be wrong, but I can see why you’d make that guess: the AD60 is an extremely long locomotive, and sometimes long steam locomotives experience ventilation problems when going through tunnels. Indeed, this was a concern for the AD60 and some were fitted with ventilation pipes, but these carried air from the front of the engine back to the cab, not from down near the wheels like this mystery pipe would. However, the pipe does connect through to the cab…

It’s worth taking a moment though to consider why this is such a long locomotive, though: you may have noticed that it exhibits a rather unusual shape! The AD60 is a Garratt locomotive, an uncommon articulated design which places a single (usually relatively-large) boiler straddled in-between two steam engines. Articulating a locomotive allows a longer design to safely take corners that were only rated for shorter vehicles (which can be important if your network rolled out narrow-gauge everywhere to begin with, or if you put too many curves onto a mountain railway). Garratt (and other articulated steam) locos are a fascinating concept however you look at them, but I’m going to try harder than usual to stay on-topic today.

And by the time you’re articulating a locomotive anyway, engineer Herbert William Garratt reasoned, you might as well give it a huge boiler and two engines and give it the kind of power output you’d normally expect from double-heading your train. And it pretty-much worked, too! Garratt-type articulated steam locomotives proved very popular in Africa, where some of the most-powerful ones constructed remained in service until 1980, mountainous parts of Asia, and – to a lesser extent – in Australia.

Indeed: it’s the combination of length of this loco and its two (loud) engines that necessitated the addition of the “mystery pipe”. Can you work out what it is, yet? One final clue before I give the game away – it’s a safety feature.

While you think about that, I direct your attention to this photo of the Я-class (of which only one was ever built), which shows you what happens then the Soviet Union thought “Da, we have to be having one of these ‘Garratt’ steam engines with the bending… but we have also to be making it much bigger than those capitalist dogs would.” What a monster!

In the 1840s, engineer Edward Alfred Cowper (who’d later go on to design the famous single-arch roof of Birmingham New Street station which lasted until its redevelopment in the 1960s) invented a device called the railway detonator. A detonator is a small explosive charge that can be attached to a railway line and which will explode when a train drives over it. The original idea – and still one in which they’re used to this day – is that if a train breaks down or otherwise has to come to a halt in foggy conditions, they can be placed on the track behind. If another train comes along, the driver will hear the distinctive “bangs” of the detonators which will warn them to put on the brakes and stop, and so avoid a collision with the stopped train ahead.

They’re the grown-up equivalent of those things kids used to be able to buy that went bang when you threw them on the ground (or, in a great example of why kids shouldn’t be allowed to buy them, at least in the case of a childhood friend of mine, detonated them by biting them!).

But when your cab is behind not only the (long) boiler and (even longer and very loud) articulated engine of an AD60, there’s a very real risk that you won’t hear a detonator, triggered by the front wheels of your loco. Your 264-tonnes of locomotive plus the weight of the entire train behind you can sail on through a trio of detonators and not even hear the warning (though you’re probably likely to hear the bang that comes later, when you catch up with the obstruction ahead).

The mystery tubes on the AD60 were added to address this problem: they’re a noise-carrier! Connecting the area right behind the leading wheels to the drivers’ cab via a long tube makes the driver more-able to hear what’s happening on the rails, specifically so that they can hear if the engine begins to roll over a detonator. That’s a crazy bit of engineering, right? Installing a tube along most of the length of a locomotive just to carry the sound of the wheels (and anything they collide with) to the driver’s cab seems like a bizarre step, but having already-constructed the vehicle in a way that introduced that potential safety problem, it was the simplest and lowest-cost retrofitting.

In other news: this is what happens when I finish the last exam I anticipate sitting in a long while, this week (I know I’ve said that before, last time I was in the position of finishing a final-exam-before-a-dissertation). Clearly my brain chooses to celebrate not having to learn what I was studying for a bit by taking a break to learn something completely different.

× × × × × ×

## Lucy`s Secret Number puzzle

Lucy’s Secret Number puzzle (datagenetics.com)

You are at a party and overhear a conversation between Lucy and her friend.

In the conversation, Lucy mentions she has a secret number that is less than 100.

She also confesses the following information:

“The number is uniquely describable by the answers to the following four questions:”

Q1) Is the number divisible by two?
Q2) Is the number divisible by three?
Q3) Is the number divisible by five?
Q4) Is the number divisible by seven?

I loved this puzzle. I first solved it a brute-force way, with Excel. Then I found increasingly elegant and logical solutions. Then I shared it with some friends: I love it! Go read the whole thing.

## 100 prisoner escape

A classic prison escape puzzle featuring 100 prisoners, 100 boxes and 100 tickets.

## Geocaching Like Batman

As the days get longer and the weather gets better, woodland trails and city alleyways alike begin to more-frequently see a particular brand of explorer. Clutching GPS devices (or, increasingly, mid- to high-end mobile phones), these satellite-guided adventurers shy away from normal people, whom they call “muggles”. Outwardly, this is out of concern for the continuity of their tiny treasure, but as often as not, it’s because geocachers – and especially urban geocachers, who often don’t even have the excuse of “getting some fresh air” to justify their hobby – are likely to be seen as a little odd., “You do what for a hobby? Find lost lunchboxes?”

I’ve written plenty about geocaching already, but the only important thing to know for this particular anecdote is how geocaches are rated to indicate how hard they are. There are two scales, each scored from one to five “stars”. The first scale is difficulty, which is about how challenging the geocache is to find – a 1-star rating means that it’s in plain sight, not camouflaged, etc., while higher ratings might mean that it’s well-concealed, tiny, disguised as something else, or requires that you solve a puzzle in order to determine where it is. The second scale is terrain, which is about how challenging the geocache is to get to. A 1-star rating is typically accessible by wheelchair – you certainly don’t need to leave paved roads and footpaths to get it; higher ratings might mean steep gradients, tree climbing, long hikes, and so on. The highest terrain ratings often mean that specialised skills or equipment are required (for example, rock climbing gear or a scuba tank).

As you can imagine, caches with a 5-star “terrain” rating are rarer, and are especially uncommon in built-up areas. Half-way up cliffs… deep inside caves… miles out to sea: these are the places you’d expect to see geocaches with the highest level of “terrain” score. So imagine my surprise when I discover GC13WZQ (“Swing Lower”), a geocache with a 1-star “difficulty” rating but a 5-star “terrain” rating, just a few minutes walk from Oxford City Centre. In the seven years this cache has been in place, it had seen fewer than 110 successful visitors: contrast to its neighbour, GCK57Z (“Swing Low”) – a virtual cache less than 10 metres away – which has seen about six times as many visits in only 3 years longer. This, I thought, was a cache I had to see.

Folks recently attempting to find the geocache had reported (OxfordLad, izybuzyfingers, twitcher50) that it had been made inaccessible by the recent addition of boards and barbed wire to the edges of the bridge. Counter-arguments were raised (sandvika, Mad H@ter) to show that this didn’t make the cache inaccessible; it merely made it accessible only by boat, which had already been suggested in the “attributes” for the cache.

I’m not a believer in the idea that any particular geocache can only be found one particular way. Also: I don’t have a boat. So I decided to make an expedition to “Swing Lower” my own damn way. Approaching the bridge under which the cache is located, I immediately saw the boards and barbed wire that had been reported by those that had attempted it earlier in the year. But as I would soon discover, anybody who was put off by a little bit of plywood and the risk of damp feet really wasn’t built of the right stuff to be able to do what was required next. Put simply: boards and barbed wire are the least of your problems when you’re hunting for GC13WZQ.

The bigger challenge was getting to the cache once underneath the bridge. I discovered (perhaps with a little inspiration from “Jackhuber”) that it was possible to brace myself against a pair of the beams that run the length of the bridge and – facing down – shuffle sideways to get to the centre of the bridge. I felt acutely aware of the fact that until I got over the central channel, the depth of the water might not be enough to break my fall (especially if I slipped and fell head-first), but was reassured by the fact that I’d brought fellow ‘cacher and coworker kateevery and she was ready, perhaps not to swim out and get me but at least to call 999, should the need arise.

So there you go. To all of you wusses for whom “there are boards and barbed wire in the way” was an excuse: you hadn’t even begun to face the challenge of “Swing Lower”. I’ve written up a Batman-themed description of the expedition as part of my log report.

This conveniently coincides with the week that I launched my new collection of puzzle geocaches, the Oxford Steganography Series – four geocaches (GC54F78, GC54F7B, GC54F7J, GC54F7N) whose coordinates are concealed within images or text, each of which contains a transparency film that can be used (I made a video showing how) to determine the coordinates of a fifth, bonus cache. I’m reasonably pleased with the series, and I’ve been enjoying reading the reports of the ‘cachers who’ve been out hunting for them, so far.

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