Author: Emily Fleming

Dice problem

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 …

Cross Stitching

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]

Latin Squares

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].

The Game of Life

From this great article in Plus magazine

Go to this https://bitstorm.org/gameoflife/ and colour in a 2 by 2 square on the screen like this:

Press start. Nothing should happen to the square. Why?

Well, because each yellow square has exactly 3 neighbours so all survive. There are no other cells that have exactly 3 neighbours so no new cells are born.

Now try with a three by three cell:

Press start. What happens?

Try to work out on paper what you think would happen for a 4 x 4 shape.

Then test your answer.

How about 5 x 5, 6 x 6 and 7 x 7?

Have a play around and see what fun patterns you can make.

You might like to read the article from Plus Maths or even try this question from the 1996 British Informatics Olympiad.