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Today we played a game where everyone simultaneously guesses a number between 0 and 100. The person who is closest to the average (mean) wins. What number would you choose?

The game is played in multiple rounds. It is interesting to see how strategies change and how the mean changes over time.

One fun variation is that the winner is the person who is closed to 2/3 of the mean – an analysis is here.

We played a game that John H. Conway he co-invented with Michael S. Paterson while they were both at Cambridge.

It is called Sprouts, and the rules are summarised by Nrich here.

You can try and discover some of the maths behind it by working through this article. We managed to prove the maximum and minimum number of moves for a game starting with three points.

We started with this warm up puzzle from Nrich:

The interactive version is here.

We then used this worksheet to explore how a disease could spread through a network. This was adapted from this set of resources from Nrich.

Take 7 playing cards.

Put them into any number of piles and arrange in descending order. For example:

Take one card from each pile to form a new pile.

Put the piles in descending order.

Keep repeating this process.

What do you notice?

Try all different combinations of 7 cards and try and represent your findings on paper. What is the longest sequence you can find?

Then try with 6 cards. What is different this time?

For more questions and solutions see our SAMI Maths Club app.

I have a 10-sided dice with sides numbered: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

I roll the dice many times until a same number has come up twice.

Example: 3, 1, 5, 6, 8, 4, 5

5 has come up twice so I stop. It took 7 rolls for this to happen.

1. How many times do I need roll the dice until I am certain to roll a same number twice?
2. What is the smallest number of times I can roll the dice before I could get a same number twice?
3. How many times do I need to roll the dice until there is a 50% chance of getting a same number twice….? Try to do an experiment to find out….

Experiment: Use your calculator (RanInt#(1,10)) to simulate a dice roll. Keep rolling until you get a same number twice. Repeat this experiment 50 times in total and complete the table below.

Or write a program in Python to do this for you.

(Using a simulation to learn about probabilities is called a Monte Carlo Simulation)

See here for a Python program and discussion of the solution and extensions …

We had a great session today working together with the Kongali Community Library Maths Camp on modulo arithmetic.

Here are the slides (as a pdf), the 1st and 2nd explorations and a fantastic geogebra app.

 

Challenge

Can you draw this curve smoothly using only a straight edge and a pencil?

You can do it by continuing this pattern:

You could try it on Python from this starting point. Note that the co-ordinates are not correct for the first segment yet!

You could even try to do it in all four quadrants:

Or at an angle:

There is an ancient art called cross stitching that uses these ideas. Instead of stitching, we could make Christmas cards for the Bazar de Noël using Python and a 3D printer … let me know your designs at [email protected]

Welcome back to Maths Club! We are so happy to be able to get together again in person.

Today we tried this puzzle from the SAMI VMC playing card deck

For a hint, the solution and extensions see here.

In these problems, which we learnt about from Maths Pickle, you will see some shapes made out of hexagons.

It might look something like one of these:

And we’re basically going to try to fill in each of the hexagons in one of three colours (red, orange or green).

Green means that from the starting point you can ALWAYS pass through all the hexagons (no matter what path you take). You can’t go back on yourself though.

Orange means that SOMETIMES you can pass through all the hexagons and other times you can’t (it depends on the path you take)

Red means that you can NEVER pass through all of the hexagons no matter what path you take.

Let’s look at an example:

Take this shape here:

If we start from the this hexagon:

We have two options of paths:

As you can see both paths pass through all the hexagons.

This means the top square is green:

Taking the same example. But starting from this hexagon:

There are 4 options of paths to take:

None of these paths pass through all the hexagons.

So the hexagon is red.

Finally if we start from this hexagon:

We have 3 options of paths:

Here some of the paths pass through all the hexagons and others don’t.

This means the hexagon is orange.

For the moment our shape looks like ths:

We want to fill each hexagon in in either red, orange or green.

Now try some of these ones to test your understanding!

Example 1:

Example 2:

Example 3:

Example 4:

Select the 16 Jacks, Queens, Kings and Aces from a pack of cards. Try to put them in a 4 by 4 square so that each rank (J, Q, K, A) and each suit (Clubs, Diamonds, Hearts, Spades) appears only once in each row and column.

This puzzle is an example of a Latin square. Latin squares are used in medical trials to ensure every participant is allocated to each treatment for the same time period to prove which is the best treatment. See these links for some more info – mathsisfun, wikipedia and nrich.

We are really missing having maths club in person, and we missed the maths camps in Africa in the summer … but we are so happy that circumstances have meant the launch of the Virtual Maths Camp. The puzzle above is going to appear on the 6 of spades in our card deck! Please check out the idea behind our maths club app  which can be accessed online here. We are very keen to translate our activities into French so that they can be used in countries like Togo. If you would like to help with translation, please get in touch with Emily Fleming at [email protected].