This blog post is about a sequence of visual perception and geometry puzzles I have created called Jenga Views. You can download a file here with 39 puzzles, roughly in order of difficulty.
In my previous blog post, I showed two variations on traditional Jenga that I think are more interesting and more fun. But long before those were thought of, I had already been doing something non-traditional with Jenga blocks.
Back in May 2018, I saw a tweet that shared a maths/art activity called Fun With Orthoprojections by JD Hamkins. It was a list of challenges where 1 by 2 by 4 wooden blocks had to be arranged to match views from the top and two sides. I thought it was really cool, but I didn’t have any blocks with those proportions. I did have a quadruple set of Jenga blocks, but Jenga blocks have very different proportions to 1:2:4, so in order to use them I’d have to make my own.
After a furious effort in Inkscape and Word over one day and night, I had made the first version of Jenga Views, where Jenga blocks had to be arranged to match views of the shape from the top and two sides. There were 20 puzzles in total: the first eleven were based on JD Hamkins’s Fun with Orthoprojections, but the later ones were all my own. (The SVG Inkscape file with the carefully measured block faces is here, if you’re ever interested in making any yourself.)
I put them out at One Hundred Factorial the next day, where they were an immediate success. Check out these two students working on one of the challenges on that very first day:
In general, over the years, I have found that the Jenga Views challenges are strangely compelling to anyone for whom they spark interest. Some people aren’t intrigued by them, but those who are intrigued tend to just stick around and do all of them, one after the other.
One thing I particularly like about them is that you don’t need an answer key, because you can just look at your construction and tell if it looks right or not. There’s something empowering about being able to check it yourself. (I’m sure there’s a lesson there for maths problems we give to students for practice, but I’m not going to explore that thought more right now.) I love watching students crouching down to see their construction from the correct angle and holding up the pictures to compare.
One of those people who found it compelling was my younger daughter Charlotte. In April 2020, she was 11 years old and only a couple of months into Year 6 (which here in South Australia is the final year of Primary School) and suddenly we all went into pandemic lockdown. My wife, who is a trained teacher, cobbled together her own school away from school curriculum for Charlotte before Charlotte’s school sorted anything out, and I provided some maths activities I had brought home with me from university. I had brought a selection of things from One Hundred Factorial home so I didn’t go insane and so I could try to run One Hundred Factorial from lockdown. One of those things was Jenga Views.
And Charlotte loved it. Because of the quadruple set of Jenga blocks, she actually had enough to do all 20 challenges separately and lay out all the answers at once.
(Note that the file has been updated since this image was taken, so don’t use it as an answer key, because almost all the numbers refer to different challenges now! Also you can tell if your solution really is one without an answer key, as I said earlier.)
Charlotte was so very proud of herself and I was proud of her. I shared the photo and the Jenga Views document on Twitter, and it got a lot of attention. There were a lot of people who were also in lockdown who were extremely grateful for something fun and mathematical to do using resources they had in their house already.
I was all inspired too, and I created more puzzles, adding five more the next day and then five more the day after that, bringing the total to 30. I also created a print-and-cut net that would allow people to make their own blocks in the Jenga proportions, since someone complained they didn’t have any in their house, as well as a video of how to fold it up into a Jenga block. (Two nets are on the last page of the Jenga Views document, if you want something better quality than this picture.)
Eventually, the interest settled down on Twitter. But over the years I’ve pulled out Jenga Views at One Hundred Factorial regularly, and every time, there’s always people who do what Charlotte did and just work through all of them.
Now we’re here five and a half years later (and seven and a half years after its original creation), and I’ve finally gotten around to writing all this up as a blog post.
To reward everyone who waited – including me – I have created nine more puzzles. They are mixed in among the 30 that were already there, so be careful if you’ve downloaded it before because almost all the numbers have changed! Also at the end of the document there are four empty challenges for you to draw your own, and the net of the make-your-own blocks too.
As an aside, the reason I did nine more and not ten is because then you can print them two-to-a-page or three-to-a-page including the title page and they will line up neatly without annoying blanks. It’s been something that’s bothered me every time I’ve printed them over the last seven years.
So there’s the whole story of Jenga Views. I hope you enjoyed reading about it, and I hope you enjoy doing the challenges yourself.
In this blog post I will tell you about two variations to traditional Jenga that I find fun, and also reflect on what these say about what “fun” means to me.
Original Jenga
It’s best to discuss original Jenga before talking about the variations, just in case there are important things about Jenga you don’t know, but also to explain why I might want variations at all.
Original Jenga is a family game of dexterity. Rectangular blocks are stacked in layers of three into a tower, with blocks in each layer at right angles to the layer below. Players take turns to pull a block out of the tower from anywhere except the last completed layer, then lay it on the top to complete new layers. If the tower falls during a player’s turn or in the few seconds afterwards, then that player loses and the game is over.
One thing that is kind of ambiguous is exactly what counts as “falling over”. Does just one block falling to the table count as falling over? If not, then how many blocks does it have to be to count as fallen? If you catch the falling blocks so they don’t hit the ground, does it count as falling? Can you catch the tower as a whole and straighten it to avoid losing? So many questions! But actually I love that there’s so many questions. It’s fun for me to have the discussion and decide together, and sometimes to have to change that decision because a situation comes up that we didn’t think of. In the end, when rules are ambiguous or missing, I follow Dan Finkel’s philosophy: “Choose what seems like the most fun way to resolve questions about the rules”. And having to resolve them is part of the fun.
Other than that little ambiguity, that’s pretty much it. You choose blocks to pull out, you pull them out and put them on top, and if you’re lucky and/or skilled, you don’t knock it over. The suspense is pretty thrilling near the end of the game, and the tower falling always sparks a cheer. But after a while, if I’m honest, it’s just not that interesting.
I think I know why: everything’s the same and there’s no creativity. All the layers of the tower are the same as each other and there are only two ways to pull out a block – pull out a side one or pull out a middle one – and putting it back on top is similarly restricted. Yes there’s suspense, but it’s always the same suspense every time, where you fear the tower will fall over. I like games to have a little more variety, and have a little more scope for creativity in the choices you make on your turn. The two alternatives below solve those two problems in different ways.
Before I talk about variations, I just want to mention two properties of the blocks that are both interesting and relevant.
The first is how many blocks there are. When it was first released and for a long time, a Jenga set was 51 blocks, which is how I know that 51 is not prime – it has to be a multiple of three since each layer has three blocks. Nowadays a Jenga set is 54 blocks, so one layer higher.
The second thing is the shape of the blocks. Because the orthogonal layers have to fit together, the blocks have to be three times as long as they are wide. There is no particular need for the thickness to have a special relationship with either of the other dimensions, but it just so happens that the thickness of brand-name Jenga blocks is one fifth the length.
(Off-brand stacking block games don’t have this thickness-to-length proportion. Most are three times as long as they are wide, but not all. The ones that aren’t manage it by having gaps between the blocks.)
It’s these proportions that inspired the first variation…
Cursed Jenga
As I said earlier, brand-name Jenga blocks have the property that the longest edge is a multiple of both the other dimensions. That means it’s actually possible to make a square out of any of the three rectangular faces, with the blocks in different orientations. I wondered what it would be like to play Jenga with the blocks in these different orientations, and Cursed Jenga was born. (A student gave it this name during the first ever game at a welcome event for new students in February 2024 where I provided the activities.)
In the traditional orientation, there are three blocks making up a square. If you put them on edge, you can line up five to make a square. If you stand them on their ends, you need to put them in a three-by-five grid of 15 blocks to make the square. Cursed Jenga alternates between these three arrangements for its layers.
An important question is whether you can actually alternate the orientations with the 51 blocks you have. If you have all three, that’s 3+5+15, which is 23 blocks, and another set of those is 46 blocks. You can achieve 51 blocks with one more layer of 5. That leaves two options: 5+3+15+5+3+15+5 or 5+15+3+5+15+3+5. You can decide which you prefer, but the first one does begin the game filling in a 3-layer on the top, which is a bit easier. If you want to go to 54 blocks, you’ll need another 3-layer which again gives you two options: 5+3+15+5+3+15+5+3 or 3+5+15+3+5+15+3+5. This is another reason to start with 5+3, because then it will work with either 51 or 54 blocks and you don’t have to change the whole thing if you discover later it’s a different number of blocks after all. (There’s another argument for why there have to be three 5-layers: the 15-layer has a multiple of 3 blocks. A Jenga set has a multiple of 3 blocks. So you must have 3 sets of 5 to make a multiple of 3 in total.)
Another important question is how to orient two successive layers relative to each other. It matches the original spirit of the game for the long lines between blocks in the 3-layers and 5-layers to be at right angles, but what do we do between a 15-layer and the other layers? Well for structural reasons, you want to avoid lines between blocks in two successive layers being parallel on top of each other. Or stated another way, you want there to be blocks in the 15-layer that touch more than one block in the layer above or below. That effectively makes your choice for you. I very much like that having a principle just decides it for you without having to remember a specific orientation.
So here’s 51 blocks all set up ready to play Cursed Jenga:
You can probably already see one of the reasons I like this version of Jenga – just setting it up involves a whole lot of fun problem-solving!
And now to play! You can keep the same rules as ordinary Jenga, but you quickly run into an issue caused mainly by that layer of 15 vertical blocks: it’s very easy to make more blocks fall out than you intended! You can’t end the game just because more blocks fell out, because you’d have to restart all the time. My solution to this involved two aspects.
First, I changed the rule for what counts as “falling over”. The definition is now that the tower has fallen when any block in the top completed layer or above touches the table/floor. You could choose a different rule, and feel free to do so, but most of the time it doesn’t really matter because usually it’s pretty clear to everyone involved that it’s all over. Indeed, another possible rule is just to let everyone vote and if the majority agree it’s fallen, then it’s fallen.
Second, I made the rule that all blocks that fall out are passed one at a time to the future players in the order of play. Each of those players can choose to just add a block they’re holding to the top rather than take a new block out. Effectively, the goal of a turn becomes to add a block to the top, and if you don’t happen to have one, you have to take it out of the tower. Alternatively, you could leave blocks that fall out where they are, seeing them all as part of the bottom layer for the purposes of the “pulling a block out” part of the turn. They’re not quite the same, because the second one doesn’t allow specific players to save up blocks for later, but still they both mean the punishment for pulling out too many blocks at once is to make it easier for the players after you. It is important to allow people to take a block out of the tower if they want, because that is indeed a fun part of the game and you don’t want to deny them that!
And that’s it. It’s more interesting during play than traditional Jenga for a number of reasons. There are more different options for the types of blocks you can pull out at any moment, and you can sometimes make the choice of whether to pull out a block at all. More variety for the choices you can make always makes a game more interesting to me. Also, the tower is much more precarious than before, making the end of the game a lot more suspenseful. Plus, it just looks weird so people come to ask what’s going on or at least do a double-take on the way past. I do like giving people something to wonder about.
Ceiling Jenga
This variant of Jenga was originally suggested by one of my MLC tutors Alexander Mackay in December 2024, and I’ve added some minor tweaks since then.
You set up the tower as usual, except the top three layers only put two blocks each at the sides, like this:
(It will become clear shortly why this is important.)
The rules are the same traditional Jenga except for two important changes:
When you put a block into the tower, you can put it anywhere and in any orientation as long as at least one part of the block is higher than it was before.
The tower as a whole is not allowed to get any higher than it started. (This is the “ceiling” referred to in the name.)
That second rule is why I set up the top three layers like I did, so that there are places to actually put the blocks that you move upwards! The first time we played, we just pushed other blocks a little out of the way to fit the new ones in, and if you feel comfortable with that, then go for it.
You’ll also have to decide about what counts as fallen down, because the concept of “completed top layer” ceases to mean quite as much as it did before. My usual rule is that the tower has fallen when any of the blocks at the highest level touch the ground, but as I said, most of the time nobody quibbles about whether the tower has fallen.
Here’s a picture of a game in action.
And here’s a different game in action. This one is with giant blocks that don’t have the thickness proportion of brand-name blocks, but that’s fine because this variant of Jenga doesn’t actually require the thickness to be anything in particular.
I really love this game. One reason is that it just looks so bizarre. Cursed Jenga looks like you’ve set it up wrong, but Ceiling Jenga looks like you’re playing it wrong. Which you are, according to the regular rules. And if people ask, you can tell them all about it.
The other reason is on every single turn you have scope to do something creative. Want to think ahead to set up gaps to put future blocks into? You can, and feel clever. Want to put a block hanging out the side, or up a different way? You can, and feel inspired. Want to see how far you can push the definitions and argue your case to the other players? You can, and feel empowered. These are feelings you can’t have in regular Jenga, and I love how such a simple-to-state rule can make them possible.
Conclusion
So there you go: Cursed Jenga and Ceiling Jenga are two variations on traditional Jenga that allow for more variation in what happens during the game, and so make Jenga more interesting and more fun. Give them a try, and do let me know how they go for you.
Because [reasons], my game Digit Disguises has been on my mind recently, and reading the original blog post from 2019, I suddenly realised I had never shared my ideas on how to introduce the game to a whole class at once.
I conscripted the game Numbers and Letters seven years ago to help promote the Maths Learning Centre and the Writing Centre at university events like O’Week and Open Day. Ever since then, it has always bothered me how free and easy participation in the Letters game is, while the Numbers game is much less so. This Open Day I had a remarkable idea: instead of stating in the rules that the goal is to achieve the target, and trying to encourage people to take a different approach, what if I just changed the stated goal! I don’t know why I didn’t think of it before, to be honest!
This blog post is about a game I invented in February 2020, the third in a suite of Battleships-style games. (The previous two are Which Number Where and Digit Disguises.)
Last year I invented a game called Digit Disguises and it has become a regular feature at One Hundred Factorial and other events. But before Digit Disguises came along, there was another game with a similar style of interaction that we played regularly, and this blog post is about that game. The game is called “Which Number Where?”
This blog post is about a game I invented this week, and the game is AWESOME, if I do say myself.
You can read the rest of this blog post in PDF form here , including game instructions and reflections on playing and creating the game. The document also contains a later blog post with instructions for how to introduce the game to a class using a smaller version of the game.
Since 2013, the MLC and Writing Centre have been doing a game called Letters and Numbers at Orientation Weeks and Open Days to create interaction with people. I tweeted a photo of one of our sessions during Open Day yesterday and it has attracted a lot of attention, so I thought I might record some details of the game for people to read if they’re interested.
