A very warm welcome to the Transum Mathematics newsletter for October 2018.

It begins with the puzzle of the month.

Five friends are talking about their house numbers. They work out that the mean is five, the mode is two, and the median is six. What are the five house numbers?

The answer is at the end of this newsletter.

September was another busy month for updating and adding to the activities on the website. Here are some of the highlights:

**Pancake Day** is a new interactive puzzle with a low threshold and high ceiling. The objective is to use the spatula (a drag and drop image) to toss the pancakes a number of times so that they end up in a pile sorted according to their size.

In addition to getting the pancakes sorted pupils could describe the algorithm or series of steps required to sort pancakes whatever their initial positions. A much more advanced to challenge is to work out the minimum number of moves for each pile. This is quite a challenging task and most probably beyond the scope of school mathematics but interesting nevertheless.

**Fraction Dissect** has proved to be a very popular exercise so a Level 3 has been added. This level features circles in which a number of parts have been shaded. The task is to calculate the fraction of the whole circle that has been coloured in.

**Unit Pricing** is a set of five exercises preparing pupils to calculate best buys, a useful skill indeed. Correct answers to each of the questions in levels one to three earn jigsaw pieces which, when all collected, fit together to make an extremely hilarious mathematical joke. Levels four and five are drag-and-drop shopping trolley activities with more complex situations.

**Cosmic Redshift** is a strange name for a mathematical activity but to explain it would be to give away the puzzle’s hidden secret. Pupils are asked to work their way through a flowchart with a number of their choosing. They should find that they always get the same answer but why? That sounds like a prompt for an investigation! As always the answer is available to Transum subscribers lower down the page.

Here’s an update on the **Trafalgar Square** puzzle which you may have read about in the last newsletter. The creators, two Slovakian brothers have been in touch. They were pleased to see photographs of their work displayed on the Transum website and have sent some more exclusive puzzles. We are no closer to solving the level 8 puzzle though. The only clue was “you all should think a bit differently”!

Don’t forget that October is the spooky, scary month leading up to Halloween. Get into the spirit (pun intended) with some of the Halloween activities that can be found on the website. You could start with **Trick or Treat**.

If you are still reading you must be a loyal Transum fan. I wonder if you could help by replying to this email with one word (or phrase). What do you use the Transum website for most often? Which section (games, Starters, puzzles, exam-style questions, Random Name Generator etc.) should I spend my time improving to better support your teaching?

Finally the answer to the puzzle of the month can be worked out as follows:

If the mode is two and the median is six then the numbers can be represented as 2, 2, 6, x, y where x and y are yet to be found.

If the mean of the five numbers is 5, then the sum of the five numbers must be 25.

2 + 2 + 6 + x + y = 25

Then x+ y = 15

x and y must both be greater than 6 and they must also be different integers. It therefore follows that x = 7 and y = 8.

The five house numbers are 2,2,6,7 and 8.

That’s all for this month,

John

P.S. Why did the mathematician think that Halloween was the same as Christmas? Because 31 OCT = 25 DEC.