The 15 puzzle

In his session about “What is mathematical proof?” on Monday 3 November Tim Gowers will mention the 15-puzzle.

Tim Gowers at CoLA, Monday 3 November

Tim Gowers, professor of mathematics at Cambridge University and a former winner of the Fields Medal (the equivalent for maths of the Nobel Prize, but awarded only once every four years), was at CoLA on Monday 3 November to lecture and lead a classroom session on “What is mathematical proof?”

Extra induction, series, and linear interpolation practice problems for FP1

These problems are designed to be simple, so that you can do them and get confidence in doing basic, simple induction, series, and linear interpolation problems.

Download the pdf here.

Solution to 26 October fortnightly prize question

You want to get from one end of an airport terminal to the other, but you must tie up your shoelace on the way. Is it quicker to tie your shoelace when you are on a moving walkway or when you are on stationary ground? (I borrowed the problem from Terry Tao’s blog.)

Deniz Yukselir won the prize, with a clever graphical solution.

Click here to see Deniz’s solution on powerpoint.

Terry Tao discusses the problem and some extensions on this web page.

In algebra: if you walk at speed v, and the walkway moves at speed u, and it takes time t to tie your laces, then the person who ties her or his shoelaces off-walkway falls (v+u)t behind the person on the walkway, and only catches up by vt when the other person stops on the walkway to tie her or his laces.

Therefore, it’s best to tie your laces on the walkway.

Hamse’s solution to the circle problem, and difference equations

1		2		4		8		16		31		57		99		163
	1		2		4		8		15		26		42		64
		1		2		4		7		11		16		22		29
			1		2		3		4		5		6		7
				1		1		1		1		1		1		1
					0		0		0		0		0		0

Martin Gardner’s “New Mathematical Diversions”

Click here to download it as pdf.

Test papers and mark schemes, October 2014

As pdfs.

Report on maths prize question for 10 October

The question was about how many regions you get if you mark n points on the circumference of a circle and draw all the lines connecting them.