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June has arrived, and so has another collection of ideas, updates and mathematical curiosities from Transum. First, let’s begin with the puzzle of the month.
Madam Mushnik was getting ready for the four-day Solvitude Festival in a land far, far away. The four best students were to be rewarded for their superb puzzle-solving skills.
The total prize pot consisted of 16 coins. The first coin was worth 1 groan, the second was worth 2 groans, and so on. The coins were to be distributed according to the Solvitude rules:
Can you find a way that Madam Mushnik could distribute the coins so that all three rules are obeyed?
If you find an answer, I'd love to hear how you solved the puzzle. Did you recognise the structure of the puzzle? Fire off an email to gro.musnarT@rettelsweN
While you think about that, here are some of the key resources added to the Transum website during the last month.
Squareas, a brand-new activity, is now available on the site. Inspired by the classic Mrs. Perkins' Quilt dissection problem, it presents students with a rectangle tiled by squares, where the side lengths of a small number of squares are given and the rest must be deduced. The puzzles are designed to encourage logical thinking and systematic working rather than straightforward calculation. There are twenty three puzzles arranged in approximate order of difficulty, with an option to reveal intermediate values once students have had a go, making it suitable for both independent work and classroom discussion.
Beam Balance is another new activity in which pupils arrange numbered treasure sacks on a beam so that both sides balance. It provides a fresh way to practise multiplication and addition while also encouraging logical thinking, trial and improvement, and careful attention to position and value. As the challenges become more demanding, pupils have to think strategically about how far each sack is from the pivot and how that affects the total on each side. It is a pleasingly mathematical puzzle with a gentle pirate flavour, and I think it will appeal to those who enjoy number challenges with a visual twist.
Pandigital Puzzles is a new drag-and-drop activity in which students arrange the digits 1 to 9 into a five-digit number and a four-digit number such that one is an exact multiple of the other. Level 1 asks for a ratio of 2, Level 2 a ratio of 3, and so on up to Level 8, where one number must be nine times the other. It sounds straightforward enough, but the trial and error involved draws students into thinking carefully about divisibility, place value and number sense without them necessarily realising it. There are hint buttons on the earlier levels for those who need a gentle nudge, and the hints gradually disappear as the levels progress.
Pandigital Squares was then created as a variation of Pandigital Puzzles. It works in a very similar way but challenges you to create square numbers.
Frustums, in six levels, is a new online exercise for pupils who are ready to go beyond the standard cone and pyramid formulae. It begins with the idea that a frustum is what is left when the top of a cone or pyramid is sliced off parallel to the base, then builds through volume, surface area and similar-shape reasoning. Later levels include more realistic problems involving cups, planters, lampshades and hoppers, giving pupils a chance to see why this slightly unusual shape is worth knowing about.
The new Unit Circle visual gives teachers a dynamic way to show how sine, cosine and tangent change as a point moves around a circle. Along with Trig Tour, this new activity offers a different viewpoint, connecting those ratios to coordinates, angles, radians, quadrants and the circular patterns behind trigonometry. It gives teachers another option when choosing how best to represent trigonometric ideas.
My use of AI (Artificial Intelligence) applications continues to grow and I keep finding new things that are great time savers. The latest one is called Wispr Flow and it lets you dictate rather than type then helps with all the spelling, punctuation and phrasing corrections. So far, I'm thinking it's quite wonderful.
The Tablesmaster statistics show that 9 × 4 is the slowest times table fact to recall (excluding the 12 times table). Just over a week ago an article in the Times newspaper reported on a much larger data set that showed 9 × 6 was the table fact most likely to cause difficulty. You can see the mean times it took students to recall all of the times table facts and the summary table from The Times on the Statistics page. What, in your experience, is the hardest times table fact to recall?
For those in many Northern Hemisphere countries the weather is starting to become warm enough to make Outdoor Maths both practical and enjoyable. The ideas on my list range from those that can be done at short notice on the playground to those that will need a little more planning and are more adventurous!
My favourite Starter this month is True or False. You can project it on your whiteboard for whole-class discussion or, if you scroll down the page, there is a student version with three levels. It provides another way to understand mathematical ideas, complementing traditional exercises.
Don't forget you can listen to this month's podcast, which is the audio version of this newsletter. Search for 'Transum Mathematics Puzzles'.
Finally, the answer to last month's puzzle, which can be seen here, Thanks so much to all who sent me an email with their solutions. Have a look in the comments below for a really wonderful method. Here is one answer (the reflection in a vertical line also works):
Extension answer
Based on this puzzle, I have developed the Knights of the Circular Table activity further as an interactive investigation. The original puzzle is still there, but pupils can now change the number of knights and the number of chairs, then investigate which arrangements have a solution and which do not. This turns the puzzle into a much richer classroom investigation, with plenty of scope for making conjectures, testing examples, spotting patterns, and asking new questions along the way.
That's all for now,
John
P.S. I put invisible ink in the printer before printing out a maths question. I couldn’t see what the problem was.
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Leonard, United States
Sunday, May 3, 2026
"My attempt to completely enumerate the 11-seat case detailed below.
"
Check for alternate solutions.
Knight 3 is Seat B.
Seat Knight 4 in Seat B :: alternate solution.
Knight 5 in Seat B.
Rick, United States
Sunday, May 3, 2026
"Here is my answer to May’s puzzle. No math, just logic, trial and error, and excel.
Since knight 1 sits in chair ‘A,’ according to the king’s rule, there must be a knight in chairs ‘B’ and ‘K.’
Assume knight 2 sits in chair ‘B.’ Then, there must be a knight in chair ‘K’ (already there) and chair ‘D.’
Let’s put knight 4 in chair ‘K,’ since it is four away from chair ‘D.’ That means there must also be a knight in chair ‘G.’
This leaves all knights positioned. We just need to see if assigning knights to chairs ‘D’ and ‘G’ will satisfy the king’s rule.
Chair ‘D’ is three away from chairs ‘A’ and ‘G’ and chair ‘G’ is five away from chairs ‘B’ and ‘A,’ so we now have all the knights successfully positioned.
Knight 1 is in chair ‘A.’
Knight 2 is in chair ‘B.’
Knight 3 is in chair ‘D.’
Knight 4 is in chair ‘K.’
Knight 5 is in chair ‘G.’
For six knights and 13 chairs, using the same method:
Knight 1 is in chair ‘A.’
Knight 2 is in chair ‘B.’
Knight 3 is in chair ‘D.’
Knight 4 is in chair ‘M.’
Knight 5 is in chair ‘I.’
Knight 6 is in chair ‘G.’
"
Richard Trimble, BlueSky
Friday, May 29, 2026