A Problem Squared

🟰 How do you round 0.44999999... to 1 decimal place? 🐟 What creative things can be done with a fish tank that has no fish? 🍂  And we have some Autumnal Other Business Head to our BlueSky / Twitter / Instagram to see some platonic solids for platonic friends, some gorgeous Welsh scenery, some diorama inspo, some toilet wine and a really old maths book. BBC Archive: The Street With Confounding Ho...

🧦 Do you put your trousers or socks on first ?👖 🎲 How much would a standard pair of dice weigh if they were made up of just protons and neutrons? 🎲 🏉 And we have some Australian Ozzie Ballness that may or may not be in the right order. Thank you to everyone who responded to our questionnaire about number and clothing ordering! All the results are in this episode. What would happen if a tables...

#️⃣ How wrong can a sequence of numbers be? 👂 What maths-related diagrams that would look good as a pair of earrings? ☕ And we have some Any Other Baristaness  Here is our dual-purpose Google Form - please answer our questions about number and clothing ordering! https://docs.google.com/forms/d/1tTb398TTacxoqlqJHGonkldwDsqnnMN6V4fRagfPOEI/ Behold the weird balls! Here is Thomas Fernique’s Instagr...

📖 What comes after thrice? ☕ How can I increase my chances of winning a free coffee? 🎹 And we have some Any Other Beatness  Thank you to everyone who sent in audio or visuals of the Thue-Morse pattern! Here is Damien’s Thue-Morse Visualiser which is really fun to play with: https://damienkee.github.io/thue-morese_visualiser/   And here is the keyboard visualisation of Thue-Morse sonified by Set...

📺 How long would it take to watch all of YouTube? 🪧 How can you make an interesting public display board without damaging the walls? 🏖️ And we have Any Other Beachness (it’s a bit windy and a bit crabby) Head to our BlueSky / Twitter / Instagram to see Matt and Bec’s differing experiences of the solar eclipse. Here’s Count Binface and Matt the Count Binface Count Agent getting papped in Clacton:...

👬 How do you know if a work-friend is a real-friend? ⭕ What would happen if Pi was 4? 😴 And we have Any Other Boring-Stories… Head to our BlueSky / Twitter / Instagram to see Bec’s selfies with The Stars of Space (real and fictional), and the cute-faced Rivian Car. Why not try Hyperbolic Crochet?! https://startcrochet.com/ultimate-beginners-guide-to-hyperbolic-crochet/ Why not try a checked 25x...

⚽ What’s the fairest way to pick teams? 🤖 How do you discourage colleagues from using AI to write everything? 🚗 And this road trip is jeopardised by playing ‘Accelerator or Break?’ Thanks to all of you who sent in answers to “what are you doing while you’re listening to A Problem Squared?” - we go through as many as we possibly can in this episode! Here is kram1032’s post on Maths Stack Exchang...

There's no new episode of A Problem Squared this week - sorry everyone - but we will be back with your scheduled Episode 140 on MONDAY 10TH AUGUST 2026, and our normal twokly service will be resumed from MONDAY 17TH AUGUST 2026. We're delaying one episode by one week due to general busyness and time-zone clashes but rest assured you will be getting your full quota of August episodes of A P...

🎺 What would standard instruments sound like if they were played under water? 🎯 What would be the average score of one randomly thrown dart? 📂 And there’s some Any Other Business. AOB.zip On THIS episode of A Problem Squared we’re joined by a special guest! The musical (and regularly quite wet) musical maestro Steve Pretty tells us all about playing music underwater - illustrated with some very...

📝 What is the perfect arrangement of black squares in a crossword? 🚣 Does weight on an aqueduct increase as a boat goes over it? 🛟 And there’s some Any Other Boardness (not ‘boredness’) Head to our BlueSky / Twitter / Instagram to see some crossword arrangements and some cross-bridge arrangements. Michael Keith’s Crossword research paper: http://www.gathering4gardner.org/g4g16gift/KeithMichael-...

👂Why do some people hate the sound of whispering? 💡 How much does an electron cost? 😎 And there’s some Any Other Bozoness On THIS episode of A Problem Squared - which comes with our special No Whisper Guarantee - we’re joined by a special guest! The clinical psychologist Dr Jane Gregory tells us all about Misophonia. You can find out about her fantastic (and very helpful) book Sounds Like Misop...

#️⃣ What’s the best way to explain the number e to an 8-year-old? 💗 How early in a relationship should you reveal that you’re a bit weird? 🤧 And there’s some any other blow-your-nose-ness Head to our socials to see The Beautiful Old Calculator and The World’s Tallest Comedian. Matt is bringing An Evening of Unnecessary Detail to New York! The Bell House, Brooklyn on Sunday 12th July. Tickets can...

🍝 Why do we put salt in pasta water? 👾 Can you put bespoke characters in to a QR Code? 🌼And Spring Has Sprung (in the UK) so there’s some Any Other Bloomsness Head to our socials to see some frankly-very-silly-but-fully-operational QR Codes. Boiling and Freezing Points of Pure and Salty Water https://van.physics.illinois.edu/ask/listing/1457 Matt has extended his tour - and filming the show in...

🤘To mark the May Birthday of Dwayne 'The' 'Tooth Fairy' 'Rock' Johnson, Episode 134 is a Tooth and Rock Special! 🪨 Matt answers your rock-based queries and shares a Salt of the Perth update 🦷 Bec and Dentist Sophie answer your tooth-based queries and shares an Adult Tooth Fairy update Head to our socials to look at some incredibly detailed Salt of the Perth imagery. And...

🥣 What percentage of a box of Weet-Bix is wheat again? 🥚 What shape is an egg?  💬 What’s the most efficient way to write your name on a Pop-it Fidget Toy? 👎 And would you like some AOB? We won’t take no for an answer Head to our socials to see all the Weet-Bix Pix, lots of names efficiently spelt out on a Pop-It Fidget Toy, lots of Girl Scout cookies, and a sheep being sheared by a robot… The...

🔠 Are there any English words containing four letters in alphabetical order? 🥣 What percentage of a box of weet-bix is wheat? 🎪 And there is some any other bah-bah-bahbahbahbah-buh-buh-business Head to our socials to see Bec’s post-show photos and videos from her Adelaide run including Morgan and Morgan's mum’s tooth, Scott and the 6-7 shirt and Karn and his incredible APS Flipchart.  You’l...

👋 When microwaving food, should you place it in the centre, or off to the side? 📐 Does the longest diagonal in a 1m sided cube in 4D square equal root 4?  🐨 And there’s some Bonus Other Business. Head to our socials to see Bec’s Photographic Exhibition of Australian Wildlife, Cubie the Moon Rover, Bec’s Poppadom Experiment,  Matt’s Pythagorean Whiteboard Action, and the first glimpse of the mos...

🌈 Is it true that "No Two Packs Of Skittles Are The Same?” 🤧 Why a cold called cold? 🤫 And there’s some ASMROB Head to our socials to see Matt’s Mission Patches, Matt’s Calculator, and the Skittles Combinatorics! The Liberation Laser Software by Seb Lee-Delisle https://liberationlaser.com/   The Skittle Maths by Clare Wallace https://www.clarewallace.co.uk/skittles And some Norfolk Punch,...

🛫 How many people are flying in the air at any given moment? ⚖️ What weighs a pound and costs a pound? 🏈 And there’s some Any Other (Foot)Ballness Head to our socials to see Bec’s glasses 🤓Pat Patriot 🇺🇲and our Pound for Pound items! Here is a link to the book Flying With Confidence (which helped Producer Laura with her fear of flying and also helped her answer the problem correctly!) https://w...

❓ Have you sent in a question for our AMA episode? ❔ Have Matt and Bec answered it in this AMA episode? ⁉️ Here are your AMA questions, answered! We’ll be back solving your problems as normal in Episode 129! If you’d like to see Bec at the Adelaide Fringe in March, you can get tickets here: https://adelaidefringe.com.au/fringetix/bec-hill-creates-the-perfect-show-work-in-progress-af2026   And if...

🫘 Can we come up with some fun names for common pantry items? 🔢 What's the smallest number that has never been written down in human history? 🧂 And there’s a sprinkling of Any Other Business. Numberphile’s take on a number NOBODY has thought of: https://www.youtube.com/watch?v=KdZrxkix9Mk Every Time "67" Has Been Said on Numberphile, if you dare: https://www.youtube.com/watch?v=Ll...

🧊 Why doesn’t the coldest day fall on the shortest day? 🥂 If you don’t drink, what can you use fancy drinking glasses for? 🏊 And we take the plunge into some Any Other Brrrrrrrness. If you’d like to read about defibrillator testing using a turkey, here’s the paper sent in by Hans: https://pubmed.ncbi.nlm.nih.gov/12879378/ If you’d like to see Matt and Bec - alongside Steve Mould and Helen Arney...

💨 How many people are needed to guarantee that there is always someone farting somewhere? 🔠 If you match each letter with the corresponding number in the alphabet and add them together, which words add up to 100. 🏁 And there is some unfinished business. Head to our socials for pictures of Matt’s Homemade Sea Salt and Bec’s Brilliant Branding, an assortment of Massive Hourglasses, the beautiful...

👼 What is the Angle of Death? 🎼 What is the best filing system for sheet music? 🎄And there’ll be some A-ho-ho-ho-B If you have any maths-studio-based-names for the Newdio, go to the Problem Posing Page at aproblemsquared.com and select ‘Solution’ and be as funny and punny as possible! If you’d like to ask Matt and Bec anything for our special 2^7 episode in February go to the Problem Posing Pag...

🍟 Why does the nutritional value of frozen chips change depending on whether they are cooked in an air fryer or in an oven? ⛰️ How large a mountain could we make from 2.2 meters of dredged sea bed (combatting sea level rise in the process)? 🃏And there’ll be some AOB, as easy as 123. Head to our socials for pics of LIVE MATHS, chip nutritional values, post-Totoro Bec, ESA Souvenirs. If you’d like...