Month: November 2019

Team Maths Challenge 2019

This week a team of four of our students went to the UKMT senior team maths challenge. The UKMT do an amazing job promoting a love of problem solving, and our students had a great time.

In maths club we tried one of the rounds (from the junior maths team challenge!) which is a crossnumber puzzle with a difference. One team are only given the down clues and the other team are only given the across clues. They then have to fill in the grid without talking.

Here is the grid.

Here are the across clues ( horizontalement en francais)and here are the down (verticalement en francais) clues. Just look at one of these and try and find someone to play with! You could fill in your shared answers on this grid.

Langford’s Problem

Take the numbers 1,1,2,2,3,3. Write them in a line so that there is one number between the two ones, two numbers between the two twos, and three numbers between the two threes.

Take the numbers 1,1,2,2,3,3,4,4. Write them in a line so that there is one number between the two ones, two numbers between the two twos, three numbers between the two threes, and four numbers between the two fours.

Take the numbers 1,1,2,2,3,3,4,4,5,5. Write them in a line so that there is one number between the two ones, two numbers between the two twos, three numbers between the two threes, four numbers between the two fours and five numbers between the two fives.

One of the above challenges is impossible – can you work out which one and prove why it is impossible?

Question and solution as pdfs in English and en francais question and solution.

Spinning points

Imagine two points spinning round a circle at the same speed.

Now imagine their midpoint. What shape would the midpoint trace out as the points spin round? Does it make a difference where the first two points start?

What would the trace of the midpoint look like if one of the points was spinning twice as fast as the other?

After trying to visualise it, you make like to use Geogebra to see if you are right. Instructions are here. For a bigger challenge, don’t use “point on object”, but just use a slider and try and create the two points using the slider as a parameter.

En francais.