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Settling Circular Debts

Saturday 1st October 2022

This is the Transum Newsletter for the month of October 2022. It begins, as usual with the puzzle of the month.

Amir owes £100 to Beth. Beth owes £200 to Chris. Chris owes £300 to Dalbir. Dalbir owes £400 to Amir. What is the minimum amount of money that must change hands in order to settle these debts, and who should pay how much to whom?

While you think about that here are some of the key resources added to the Transum website during the last month.

A new video was filmed to go into the help section of the HCF and LCM exercise. The video shows a number of different ways of finding the highest common factor and lowest common multiple of two numbers. It then goes on to show a little known method of finding the HCF and LCM of three numbers and ends with a suggested method for finding the pairs of numbers with a given HCF and LCM.

Substitution Sort is a brand new activity showing that expressions need to be sorted into different orders of size depending on the value that is substituted as the variable. It provides a little more interest than a straight-forward exercise on substitution particularly if students try to guess the order before doing the substitution.

I reckon these new Yohaku Puzzles will be useful in Year 5 all the way up to Year 11. I particularly like the multiplication ones as they can be solved using knowledge of factors and prime numbers.

Yohaku Puzzles

I have uploaded a new instructional video to go with the online exercise 'Equation of a Line through Points'. I hope it will be useful for students who get stuck doing their homework. They will be able to see it when they click the Help tab as they work through the levels of the exercise.

Equation of a Line through Points

Don't forget you can listen to this month's podcast which is the audio version of this newsletter. You can find it on Spotify, Stitcher or Apple Podcasts. You can follow Transum on Twitter and 'like' Transum on Facebook. If you have any comments about this podcast please contact me at

I received an email on behalf of Corp Today Magazine, to inform me that Transum Mathematics has won: Most Engaging Mathematics Teaching Resource 2022. Lovely!

Finally the answer to last month's puzzle which was to evaluate 8 ÷ 2(2 + 2):

The correct answer 16 and the other commonly given answer is 1. Both answers can be argued to be correct however and you could say that the expression is ambiguous. In fact merely relying on BIDMAS is not enough to remove the ambiguity.

Wil sent me this from Mathematical Pie of Summer 2020:

Mathematical Pie Summer 2020

The best explanation I have found is in a video produced by Presh Talwalkar, creator of Mind Your Decisions, and can be found here.

That's all for now,


I rushed into the local fish and chip shop and asked them what 15 times 12 was. They said they only do takeaways.

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