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This is the Transum Newsletter for the month of July 2026. The Puzzle of the Month is based on a classic puzzle which I have rewritten.
Mrs Brambleshaw kept a market stall where she sold apples in three sizes: large apples at £1 each, medium apples at two for £1, and small apples at three for £1. Two medium apples weighed the same as one large apple, and three small apples weighed the same as one large apple.
Mr Barnaby Pickles had a large family. He had the same number of boys as girls, and the youngest children were twin boys. All of children, except the twins, had a birthday in a different month of the year.
He gave his children £7 to spend altogether on apples from Mrs Brambleshaw's stall. If the apples were shared equally among the children, with no apples cut up, how many young Pickles were there?
If you get an answer, I'd love to hear how you solved the puzzle (or your students solved it). Fire off an email to gro.musnarT@rettelsweN
If you enjoy the Puzzle of the Month you might also like the Advanced Starters. I frequently add new challenges and the latest addition is already one of my firm favourites. Have a look, it's called Ostrich Shadows.
While you think about that, here are some of the key resources added to the Transum website during the last month.
The Gradients activity is now steeper! What I mean by that is there are now six levels instead of two. The new higher levels include parallel and perpendicular lines along with some questions based on road signs that show gradient as percentages or ratios. The Help tab contains both a video and an infographic and a jolly jingle congratulates the student who completes a level.
A new Similar Triangles exercise has been added to Transum. It focuses on the key ideas of matching corresponding angles, identifying corresponding sides, finding scale factors and calculating missing lengths. It is intended to build confidence with triangle similarity before pupils meet the broader ideas in the existing Similar Shapes activity, which also includes area factors and volume factors. The new exercise begins with accessible visual questions, then moves on to short-answer problems where pupils need to apply the same reasoning without relying on diagrams.
Another new self-marking exercise called Intersecting Chords has been added to the website. Pupils use circle diagrams to find missing lengths, starting with intersecting chords inside a circle and progressing to secants meeting outside the circle. It is a colourful way to practise a theorem that often appears in exam-style questions but can easily be confused without plenty of diagram-based practice.
Comparing Data: GCSE Maths questions on this topic often ask pupils to compare two data sets by writing sentences about averages, spread and the shape of distributions. That is not easy for software to mark, so this activity takes a different approach. Pupils are given ready-made statements and have to decide whether each one is 'True', 'False' or 'Cannot be determined' from the information shown. The levels include summary statistics, raw data, frequency charts, stem-and-leaf diagrams, box plots, cumulative frequency graphs, histograms and a scatter graph, giving pupils plenty of practice at making careful, evidence-based comparisons.
A new Advanced Maths Crossword is now available on the website. It includes a range of mathematical terms from algebra, geometry, probability and more, with clues designed to test both vocabulary and understanding. Students can type answers directly into the grid and check their progress as they go. It is aimed at older or more confident learners (A-level or IB Diploma) who enjoy a mathematical challenge.
For decades I have remembered that on Windows, holding down the Alt key and typing 246 on the numeric keypad gives the division sign, ÷. My little memory trick was that 246 is simply the first three even numbers. Only this week did I discover that Alt 227 gives π (depending on the code page/settings), and I now have an even better way to remember it: 227 looks rather like 22/7, the famous approximation for pi. This was not, as far as I can tell, a clever decision made by someone designing the old IBM PC character set; it appears to be just a coincidence. But what a very pleasant coincidence it is!
As the end of term approaches, Transum has a wide range of free mathematical activities that require very little preparation and are perfect for those final lessons when not every student may be present and traditional work does not feel quite right. These games, puzzles, quizzes and investigations offer a chance to do something genuinely mathematical while also raising the profile of maths as an exciting, interesting and intriguing subject. The activities shown here are just some of the end-of-term suggestions, so have a look at the End of Term main page and choose something that will suit your group, whether you want a whole-class challenge, group work or individual activities.
Here are some dates in July with loosely related maths activities:
2 July :: World UFO Day :: Go
4 July :: US Independence Day :: Go
11 July :: World Population Day :: Go
14 July :: My Birthday :: Go
Variety is the spice of a good maths lesson!
Don't forget you can listen to this month's podcast, which is the audio version of this newsletter. You can find it here, on Spotify, YouTube or on Apple Podcasts. You can follow Transum on Bluesky, Twitter (some call it X) and like Transum on Facebook.
Finally, the answer to last month's puzzle, which was:
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?
Did you realise that this puzzle is closely related to 4 by 4 magic squares? If you take any 4 by 4 magic square, its rows and columns represent the days and students as a solution to this puzzle. To test this idea I have created a drag-and-drop interactive called Solvitude Festival.
Many thanks to all those people who wrote in, indicating that they had realised this connection, which means there are lots of different solutions. Have a look in the comments below for some ideas.
That's all for now,
John
P.S. If you have 12 apples in one hand and 7 oranges in the other hand, what do you have?
Big hands!
Do you have any comments? It is always useful to receive feedback on this newsletter and the resources on this website so that they can be made even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
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Transum,
Friday, June 2, 2017
"Here's a clue for one solution to last month's Puzzleof the Month. In the year 1514 the German artist Albrecht Dürer created an engraving called Melencolia with a magic square in the background. The image below shows an enlargement of the magic square. The date appears in the bottom row of the magic square.
Chris from Scotland also thought about this engraving when he sent in his solution to the puzzle of the month. He said "Take the top row to be the number of groans awarded to the first pupil each day, the second row shows what the second student gets (and so on). That’s just one way to our square but it’ll certainly ensure that each student gets 34 groans in total and that there are 34 groans issued each day!""
Mala, New Zealand
Friday, June 5, 2026
"
Wil, UK
Friday, June 5, 2026
"At first I fiddled around a bit, having realised that 34 came into it [½ x 16 x 17 /4] and then realised that the answer was a 4x4 magic square. Since I couldn't remember how to create one I looked on the internet and for example (out of the 880 possibilities — in fact 8 x 880, because we can rotate and reflect a solution) one solution is below and we can regard the rows as the values of the four coins that boy 1, boy 2, boy 3, boy 4 receive each day and the columns as the values of the coins received each day.
Rick, France
Friday, June 5, 2026
"Greetings from Paris. Here is my answer to the June puzzle. After reading the rules, I realized this was nothing more than a 4x4 magic square. Below is my solution, which I remembered from my youth, and entered in to Excel to verify. Magic square 4x4