More Lovely Puzzles!

A consistently popular post on this blog is ‘Lovely Puzzles‘ which has links to many puzzle sites which include mathematical puzzles. This seems a good time of year to investigate some of these further. A good puzzle for Christmas Eve perhaps (or any day!) would be ‘Make 24’.

Make 24 (1)

Can you make 24? You must use all the numbers once and you are allowed the four operations and brackets.
(Further information and solutions for Make 24 and other Number puzzles are listed on the Number page on Mathematics Games). Number puzzles like this can make excellent starters.

Other possibilities for puzzle-type lesson starters come from Erich Friedman who has a variety of Mathematical Puzzles; try his Weird Calculator Puzzles for example or these Number Formation Puzzles both of which would make ideal ‘Bell Work‘.

Untangle - Simon Tatham
Another great collection comes from Simon Tatham, I have been enjoying his ‘Untangle’ puzzles (which I must remember for the next time I teach Graphs in Decision Mathematics!); it is possible to change the number of nodes – use the Type menu.

Whilst many teachers use Suduko and Kenken type puzzles (note that teachers can sign up to receive free weekly KenKen puzzles), perhaps less familiar is Rogo which is very easy to learn.

This post has taken some considerable time to write as I have been very happily distracted by all these lovely puzzles – including joining the dots (from Conceptis Puzzles) something I used to love doing as a child!

Spirograph

As a child, a favourite toy was my Spirograph with which I could generate endless pretty curves! Speaking of my favourite toy, there is a wonderful electronic version available.


The Nrich problem ‘Making Maths: Planet Paths‘ challenges students to draw some planet paths using a Spirograph. In case there is no Spirograph to hand they give instructions for making a simple one.

Spirograph
Spirograph – Desmos

Alternatively, try an online version. Try Spirograph on the Desmos Graphing calculator.

Spirograph - Autograph Activity
Spirograph – Autograph Activity by Owen Elton

Owen Elton has written an excellent Spirograph Autograph activity (see Simon’s comment below) and also available on the Autograph player a very impressive 3D Spirograph!

On GeoGebra, there are various applets available, for example:

A little problem – solutions

If you have just read ‘A little problem for the holidays…

The clue is to stop thinking about the Maths and find your inner child!

Let’s reorder the numbers, does that help?

Why has 8809 been assigned a value 6 and 0000 a value 4?
What about all the numbers assigned a value of zero?

Scroll down for the answer …….

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The value assigned to 2581 should be 2 as there are two closed loops!

A little problem for the holidays….

My son sent me the following problem which I have since discovered has been doing the rounds on the Internet.
I cannot find the original source – thank you whoever originally posed the problem!

This problem can be solved by pre-school children in five to ten minutes, by programmers in an hour and by people in higher education ….well, check it yourself!

I’m pleased to say despite my various Maths degrees I solved the problem quickly!
I obviously have the mind of a pre-schooler!
You can find a hint then check the answer here.

I present the problem as posed everywhere – though it looks like a misuse of the = sign!

The problem reminded me of some fun sequences to try with your students!
Get them thinking outside that box!

Try these ….

2, 3, 3, 5, 10, 13, 39, 43, 172, 177, …

2, 12, 1112, 3112, 132112, 1113122112, ….

For the answers and several more puzzles see Puzzle Sequences from the Online Encyclopedia of Integer Sequences.
See also this post on Sequences for further resources.

More puzzles resources.