In the days before Wikipedia and Google we might refer to an encyclopedia to find answers to our questions. The puzzle for this newsletter is based on a set of ten volumes of an encyclopedia on a bookshelf arranged in order with volume one on the left and volume ten on the right.

A bookworm eats through from the front cover of volume one to the back cover of volume ten. What is the length of the bookworm’s meal if each encyclopedia is 5cm thick (the pages are 4cm and each cover is 0.5 cm thick)?

The answer is at the end of this newsletter but, be warned, it is not the obvious answer.

This puzzle is a version of the February 2^{nd} Starter of the Day which presents a random number of encyclopedias and randomly generated measurements for the pages and covers. It provides an opportunity for pupils to engage in some decimal addition and multiplication before being surprised by the actual answer.

Now the pages on the Transum website should be a little easier to find as the search facility has been upgraded. Now when you search for a term you get two sets of results. The first is directly from the Transum database and is a search on page titles and descriptions. Lower down the page you will see the Google search results which include snippets of text found on the pages.

You may like to try out the new search feature to find this month’s new additions. Firstly the Car Park Puzzle challenges you to get your car out of the very crowded car park by moving other cars forwards or backwards. It is the Transum version of a puzzle that has been available in different formats for many years but the real challenge for students is to devise a level 6 puzzle that is possible but requires more moves than level 5. The way the students record moves and consider the advantages of working backwards (doing and undoing) give this challenge a strong mathematical connection.

Polybragging is another new activity that is also based on an idea that has been around for a long time. This is a game for two or more players. Each played needs a tablet, computer or smartphone with the page loaded.

If you have ever played a card game called Top Trumps you will know the main idea of this game already. Each player is given a shape that the computer selects at random. The players each choose a shape property and whichever player has the highest value for that property wins a point.

The properties available include the size of the largest interior angle, number of pairs of parallel lines, number of lines of symmetry and the order of rotational symmetry.

Hopefully, by playing the game, pupils will develop more familiarity and a greater knowledge of the properties of polygons.

Other new additions to the site include a Dice and Spinners page to use if you can’t find the real things and a Reaction Time activity which collects data about how quickly we recognise even compared to odd numbers.

Finally some more traditional Maths exercises have been added. These include Multi-step Problems and Decimal Times. These exercises are self-marking, printable and every pupil gets a slightly different version thanks to the in-built random number generator.

Thanks to everyone who has added comments and suggestions to the site this month. Your input keeps the site alive. One comment waiting for your opinion is that made by Leslie Jackson on the 16^{th} December Starter page. Do you think powers of two are 2, 4, 8 .. or do you think they are 4, 9, 16 …?

Finally the answer to this month’s puzzle. The answer is not 50cm surprisingly. If you picture the ten volumes arranged on the shelf you will notice that the front cover of volume one is actually on the right, next to volume two! So if the bookworm starts by eating through that cover it has missed the pages and back cover of volume one altogether. Similarly the back cover of volume ten is on the left so the bookworm stops before eating the pages and front cover of volume ten.

The correct answer is 50cm – 2(4cm + 0.5cm) = 41cm

Enjoy October and don’t miss the Halloween Starter at the very end of the month.

John

ps What do you get if you divide the circumference of a Halloween lantern by its diameter?

A: Pumpkin Pi