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Weighted Puzzle

Friday 1st July 2022

At last we have arrived at the month of July, my favourite month. It has throughout my life featured wonderful times such as ‘School’s Out’ celebrations, holidays, my birthday, good weather(?) and I’m still buzzing after my 1985 experience at Wembley watching Live Aid. I hope July is packed with good things for you too.

This month’s puzzle is about an old-fashioned set of balancing scales. I have four different weights marked in pounds and can weigh any object (with an integer weight in pounds) from 1 to 40 pounds. What could those four weights be?


The answer will be in next month’s Newsletter but do send me a message if you figure it out before then.

My feeling is that even though imperial units receive a ‘lighter touch’ in schools today the topic still has ‘general knowledge’ value and can produce some nice problem-solving opportunities. Having said that I must emphasise that there are some really old imperial units that probably should stay in the history books but there are others that are used in preference to metric units in many places around the globe.

I have recently created a new set of online exercises on the less obscure imperial units and hope students enjoy solving the problems they contain.

Imperial Units Learning Resource

In the podcast version of this Newsletter I have included a short audio clip of Matt Parker's list of many imperial units and their comparisons. I found it fascinating to listen to and I hope you do too.

Another new activity to have been added to the Transum website is an interactive version of the classic Egg Timer (or hourglass) puzzles. So far many people have earned trophies for levels one to five but absolutely no one has managed to earn a trophy beyond level 5. These higher levels have a twist (that’s a clue) but no peeping at the answer until you have had a go yourself.

Egg Timers Puzzle


Two new videos have been created and uploaded specifically designed to help students complete online exercises. The first was on Standard form and the second on Three-dimensional Trigonometry.

As we approach the end of the school year I would like to remind you of two recently-updated collections containing a wide variety of resources:

End of Term Maths

End of Term Maths Learning Resources

Wouldn't it be sad if those last Maths lessons of the Term were wasted. Quite often special school activities take place during the last week of Term and as a result some pupils are taken out of normal lessons leaving you, the teacher with only two thirds of your normal class and an expectation to do something different.

It would be a crime if you put on a video (unless it was a Maths video) or simply told the pupils to get on with their own pastimes when there are so many out-of-the-ordinary mathematical activities you could be doing. Click here to see hand-picked selections of activities that have worked for me in the past and would be great fun for you to try with your classes at the end of this Term.

School Holiday Activities

Holiday Maths Learning Resources

Students are encouraged to continue their learning during the holidays. Research indicates that by the end of the long summer holiday pupils perform, on average, one month behind where they left off in the spring.

Here are some suggestions for activities that will keep children thinking mathematically while having fun and learning new skills.

You can give a link to this page to all of your pupils and even if only half a dozen of them take up the challenge that’s better than nothing.

Let me know if you have other ideas.


The Starter of the Day for 4th July is themed on American Independence Day. It’s ironic that most of the American students who might appreciate the reference won’t be in school on that day so won’t see it!

Starter of the Day


Finally the answer to last month’s puzzle. I did not receive a single correct answer so I’m hoping that the answer I have in mind is correct.

The puzzle was not which number is first if all the natural numbers are arranged in alphabetical order? Instead, it was which number is second if all the natural numbers are arranged in alphabetical order?

My answer is eight billion!

Enjoy your July,


P.S. What would the speed limit on the road near your home be if speed was measured in furlongs per fortnight?

Home :: Previous Newsletters :: Podcast

Jonathan, California

Friday, July 1, 2022


Rick Blair,

Thursday, July 14, 2022

"My answer for the July 2022 puzzle is 1, 3, 9, and 27. Ironically, these are all powers of 3."

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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