Lycee Francais SAMI Maths Club

Consider a single player card game with a standard 52 card deck.

You shuffle the cards and turn over the top card.

If you turn over a black card, you win £1. If you turn over a red card, you lose £1.

You can keep turning over cards as long as you want to.

It is impossible to lose money in this game; if you have turned over more red cards than black cards, you can just keep turning over cards until the end of the deck to end up at net £0. If you stop turning over cards before reaching the end of the deck, you keep the money that you have won up until that point.

Is there an optimal strategy for this game?

We played several games of this in maths club just with 10 cards (5 red and 5 black), keeping track of our winnings to start to guess at the best strategy.

Mr D. R. Kaprekar was an Indian school maths teacher who loved playing with numbers. See if you can follow these steps to find out what he discovered …

Choose a four digit number where the digits are not all the same (that is not 1111, 2222,…).

Rearrange the digits to get the largest and smallest numbers these digits can make.

Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

What do you notice?

Does something similar happen for 3 digit numbers? Can you prove it?

Here are pdfs of the problem in English and French.

Try it out here

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.

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.

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.

Can you solve this puzzle (French version) from our maths club pack?

Solution in English and French.

Today we tried a lovely puzzle from Alex Bellos’ column in the guardian.

The interactive app on Scratch was very helpful.

3 to the power of 2001 is a very big number (954 digits long!!). A regular calculator will not be able to calculate it.

Without calculating the value of this number, can you find the remainder when it is divided by 7?

For more explanation see the English and French versions of the puzzle.

And here are the solutions in English and French.

This problem was posted originally on the Nrich website .

The rugby world cup is up and running. If you walked in half way through a game and saw that Scotland had 21 points (if only!), you would not know whether they had scored 7 penalties or 3 converted tries.

What is the highest score that you could know exactly how the points have been scored?

For more explanation see the English and French versions of the puzzle.

And the solutions in English and French.

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We found this puzzle in Alex Bellos’ great column in the guardian.