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.


Whether you want to work out some simple calculations or compute the eigenvalues and eigenvectors of a matrix there is probably a free online calculator to do the job for you!

WolframAlpha is so powerful (and not only for Mathematics) it deserves pages of its own. There are several links available and also slideshows to help you learn to use WolframAlpha. (WolframAlpha is still entirely free to use and so useful for teachers and students, though a new Pro option is now also available).

Using WolframAlpha widgets makes it possible to set up widgets for repeated use, older students for example need to solve absolute value equations.

When I find a new online calculator I like I include it in the Calculators section of Mathematics for Students.

To highlight a few of the calculators I have used recently. For students studying quadratic equations this calculator which shows the use of the quadratic formula from Math Warehouse is very useful as it shows full working on how to use the formula.

There are numerous other calculators available from Math Warehouse.

The graphing calculator I return to again and again is the Desmos graphing calculator, for example, I was recently studying the modulus function with my sixth form students, looking at modulus equations and inequalities a picture speaks a thousand words! (Just type y=abs…)

When marking the Further Mathematicians’ Decision Mathematics paper I found Stefan Waner’s Simplex Tool very useful,

The tableaus are shown in full.

Revision and Mobile Phones…

The exam season approaches and I have been talking to many students about revision. We were chatting about the fact that they always have their phones with them…so an experiment.  Would it help to look at some basic facts on your phone on the bus / train on the way to school or wherever? I know this displays well on a Blackberry,a Windows phone on Android and an iPhone.

Common integrals (that are not in the formula book for my students).

(Integration – for a pdf file.)