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This is the Transum Newsletter for October 2016, the 10th month of the year. Have you ever noticed that the month name begins with the suffix ‘Oct-‘ suggesting eight and not ten. There is a reason for that and a quick internet search will reveal it to you.

Let’s begin with the puzzle for this month which is about three hungry children.

There was a short queue in the school canteen. Ayden was directly in front of Betsy who was directly in front of Carl.

Aden’s age is an even number but Carl’s is odd. Is a person with an even age directly in front of a person with an odd age? The answer is at the end of this newsletter.

I am very keen to tell you about some of the new additions to the Transum website that appeared last month. The first is Maths Mind Reader. Absolutely everyone I’ve used it with have been extremely impressed with this clever web page. As a Transum subscriber you will be see the mathematics that makes it work and Secondary pupils should be able to understand and even prove the concept.

A Transum website visitor, Les Page, sent me an addictive little puzzle he has devised called Zygo. He has kindly allowed a Transum interactive version to be created which is now ready to improve the numeracy and problem solving skills of your pupils. Thanks Les.

Pupils quickly learn to recognise and name regular polygons but the new activity called Polygon People may help younger pupils to name irregular polygons too. The activity has three levels and only accepts the correct spellings.

For the older pupils (14+) the Completing the Square and Proof of Circle Theorems activities should support those entered for the higher tier of the GCSE exams (or equivalent).

At times when I have not been creating new content for the website I have had a small amount of time to look at an updated app that I have downloaded to my iPhone. Photomath has been around for a couple of years but I’ve been very impressed with the recent improvements. You point your phone camera at an equation, and it will give you the answer and show you the working. I’m still amazed it can read my handwriting!

Photomath supports arithmetic, integers, fractions, decimal numbers, roots, algebraic expressions, linear equations and inequalities, quadratic equations and inequalities, absolute equations and inequalities, systems of equations, logarithms, trigonometry, exponential and logarithmic functions, derivatives and integrals.

My only reservation against using it with pupils is some of the phrases used to explain the stages of solving an equation. "Move constant to the right side and change its sign. Move variable to the left side and change its sign" is less helpful than the notion of doing the same thing to both sides in my opinion. The answer to this month’s puzzle is yes. We don’t know Betsy’s age but we do know it is either even or odd. Let’s consider the two possibilities. If Betsy’s age is odd then Ayden (even) is in front of Betsy (odd) and the answer is yes.

If Betsy’s age is even then Betsy (even) is in front of Carl (odd) and the answer is yes.

So regardless of Betsy’s age, the answer is always yes.

A similar problem was devised by Hector Levesque and it was included in Alex Bellos' Guardian blog. Unbelievably 72 per cent of the 200,000 people who answered the question got it wrong.

That's all for this month.

John

P.S. Why do mathematicians think that Halloween and Christmas are the same?

Because 31 OCT = 25 DEC (You need to know about the octal number system to understand this month's joke 31_{8} = 25_{10})

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