Digimoji

Enthusiastic Teacher,

Friday, October 10, 2025

"It's a really great idea to play each level of the Digimoji puzzle many times!

Why? Because every time you start a level, the computer randomly mixes up which emoji stands for which number.

Imagine if you had a puzzle that always used the same pieces to make the same picture. Once you solve it, it's easy the next time, right?

But in Digimoji, the puzzle changes! You can't just memorize the answer. You have to use your super-smart logic skills all over again to figure out the new secret code. Playing many times is like giving your brain a fun workout. It helps you get faster and better at cracking the code and understanding the maths, which makes you an awesome problem-solver!"

Transum,

Sunday, October 12, 2025

"If this game catches your interest, take a deeper look at its essence. Have a read of David K. Butler’s articles - Introducing Digit Disguises - he the game which inspired Digimoji. In one paper he noted that he wondered about all these questions, but explored only some:

🟰 How many questions do you need to finish the game? Is there an algorithm that will finish in the
smallest number of questions possible?
🟰 What if the goal was to correctly identify just one number? How quickly can you find the first number?
🟰 Which number is the easiest to find? Which number is the hardest?
🟰 Can you identify all the numbers using only one operation, such as only using subtraction? What is the smallest number of questions to finish the game if you're only using each operation?
🟰What if the operations were mod 10? You wouldn't be able to subtraction to tell you greater or less than in this case, but would it still be possible to find everything?
🟰 What if you had 0 to some other number, like 0 to 25 or 0 to 5. How long would the game be then? Would your strategy be any different?
🟰 What if you didn't have 0 or 1? What if you had some negative numbers? What if you had some completely other collection of numbers?
🟰 Is it even possible to find all the numbers if you have a different collection? Are there collections of numbers any size you like where you can't find any of them? Are there collections of numbers where you can find some but not others?
🟰 For the previous question, if there are only a small number of numbers (like two or three of them), what are all the sets of numbers that can all be identified?"

David Butler, BlueSky

Sunday, October 12, 2025

I had a go using only subtractions. These ten results were enough to figure which digit 0 to 9 had which emoji disguise.

[image or embed]
— David K Butler (@davidkbutler.bsky.social) October 12, 2025 at 1:47 PM

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Instructions Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

	You are learning this because future ideas are built on previous ideas and the more ideas you learn the more power you have to learn anything, ever! The world's best football player engages in rigorous training, practicing skills repeatedly to prepare for the big game. While the specific actions rehearsed during these exercises are rarely needed in the match, the very process of performing these drills enhances their overall prowess as a top player. more...	More Activities: Maths Map Go Maths Games Puzzles Times Tables TablesMaster iPad Maths Investigations Exam Questions
Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School: "Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work." Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"		Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
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Go Maths Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths Map Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.
Teachers
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Enthusiastic Teacher, Friday, October 10, 2025 "It's a really great idea to play each level of the Digimoji puzzle many times! Why? Because every time you start a level, the computer randomly mixes up which emoji stands for which number. Imagine if you had a puzzle that always used the same pieces to make the same picture. Once you solve it, it's easy the next time, right? But in Digimoji, the puzzle changes! You can't just memorize the answer. You have to use your super-smart logic skills all over again to figure out the new secret code. Playing many times is like giving your brain a fun workout. It helps you get faster and better at cracking the code and understanding the maths, which makes you an awesome problem-solver!" Transum, Sunday, October 12, 2025 "If this game catches your interest, take a deeper look at its essence. Have a read of David K. Butler’s articles - Introducing Digit Disguises - he the game which inspired Digimoji. In one paper he noted that he wondered about all these questions, but explored only some: 🟰 How many questions do you need to finish the game? Is there an algorithm that will finish in the smallest number of questions possible? 🟰 What if the goal was to correctly identify just one number? How quickly can you find the first number? 🟰 Which number is the easiest to find? Which number is the hardest? 🟰 Can you identify all the numbers using only one operation, such as only using subtraction? What is the smallest number of questions to finish the game if you're only using each operation? 🟰What if the operations were mod 10? You wouldn't be able to subtraction to tell you greater or less than in this case, but would it still be possible to find everything? 🟰 What if you had 0 to some other number, like 0 to 25 or 0 to 5. How long would the game be then? Would your strategy be any different? 🟰 What if you didn't have 0 or 1? What if you had some negative numbers? What if you had some completely other collection of numbers? 🟰 Is it even possible to find all the numbers if you have a different collection? Are there collections of numbers any size you like where you can't find any of them? Are there collections of numbers where you can find some but not others? 🟰 For the previous question, if there are only a small number of numbers (like two or three of them), what are all the sets of numbers that can all be identified?" David Butler, BlueSky Sunday, October 12, 2025 I had a go using only subtractions. These ten results were enough to figure which digit 0 to 9 had which emoji disguise. [image or embed] — David K Butler (@davidkbutler.bsky.social) October 12, 2025 at 1:47 PM Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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