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Palindromic Numbers

Wednesday 1st February 2023

This is the Transum Newsletter for the month of February 2023; the month you can celebrate Valentine's Day (14th), Pancake Day (21st) and a Palindromic Date (3rd). Talking of palindromes here is the puzzle of the month.

Mr Wheeler was on a long drive when he noticed that his odometer showed 15951 miles which is a palindromic number. The next time he saw a palindromic number on his odometer was exactly two hours later. What was his average speed during those two hours?

Rear view of a man driving a car

Let me know your solution and method for solving this puzzle and all will be revealed (including the credit for this puzzle) next month.

By the way there are more activities linked to this theme on the newly-created Number Palindromes page.

Occasionally I am made aware of a gap in the coverage of the resources provided online and I make it a project to fill that gap. The latest example of this is Algebraic HCF and LCM. Altogether there are ten levelled exercises of 12 questions each though the higher levels go beyond the expectations for most pupils. Those higher levels are based on exercises found in Maths textbooks written over one hundred years ago and provide a worthwhile challenge for the higher achievers.

Algebraic HCF


The Gradient of a Line exercise now has a Level 2 (thanks subscriber Mandy for the suggestion). This new level features straight lines drawn on axes where the vertical scale is different from the horizontal scale. Some of the labelling is obscured too making it an interesting challenge.

Abby suggested some questions about the equations of straight line graphs that are parallel to the axes so now may I present Graphs of Vertical and Horizontal Lines.

Graphs of Vertical and Horizontal Lines


A help video has been added to the Place Value exercise. When I made it I pictured it being helpful to Secondary students whos memory of learning place value in Primary school was vague or non-existent. It quickly goes through the basics then focusses on how to answer the questions in the online exercise.

I began experimenting with ChatGPT in December as you may remember from that awful poem in the last Newsletter. In early January I asked for ten questions to be generated by the computer using artificial intelligence (a generative pre-trained transformer). The software reacted to the input "Create a set of 10 interesting questions to practice working out compound interest ordered from easiest to hardest". I’ve included those questions as a new Level 6 for the Compound Interest exercises. I don't think they are particularly interesting but they do show progression in the sophistication of the calculation required.

Talking of AI I wonder if you noticed ... the picture of the guy driving a car that appears above with the puzzle of the month is a little unusual. It was generated by AI in response to the description of the puzzle I typed into MidJouney. I must say it is an absolutely wonderful service but for some reason it has trouble with the hands. Did you notice that the hands looked strange?

I have just added a Level 6 to the Upper and Lower Bounds exercise. It focuses on finding the bounds of algebraic expressions after the given substitutions. It'll give the brain and the calculator a serious workout!

The Surds exercises have been given an upgrade. There is now an eighth level and a long help video. I really won't be expecting anyone to watch the video from beginning to end but the levels have been timestamped so when you open the help tab from any of the levels you will be directed to the relevant part of the video.

Surds Learning Resource


The Currency Exchange exercises now have the latest exchange rates updated daily instead of monthly. Not sure if students will burst with excitement but I'm somewhat more satisfied.

Finally the answer to last month's puzzle which was:

A teacher writes six words on a board: “cat dog has max dim tag.” She gives three students, Arshad, Billy and Chloe each a piece of paper with one letter from her favourite word in the list (they each have a different letter from the same word). Then she asks, “Arshad, do you know the word?” Arshad immediately replies "yes". She asks, “Billy, do you know the word?” He thinks for a moment and replies "yes". Then she asks Chloe the same question. She thinks and then replies "yes". What is the teacher's favourite word?

The answer is Dog. Arshad knows right away because he has one of the unique letters that only appear once in all the words: c o h s x i. So, we know the word is not “tag.” All of these unique letters appear in different words, except for “h” and “s” in “has,” and Billy can figure out what the word is from the unique letters that are left: t, g, h, s. This eliminates “max” and “dim.” Chloe can then narrow it down the same way. Because there is only one unique letter left, the letter “d,” the word must be “dog.”

(For more on this answer, watch the video from Mind Your Decisions). The puzzle was adapted this problem from the puzzle "Yes, Yes, Yes" in "The Great Book of Mind Teasers & Mind Puzzlers" by George J. Summers, which has the same situation with 5 words.

That's all for now,


P.S. What do you need to calculate the distance around a circle of sheep?

Answer: Shepherds’ Pi.

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