Question 1

Write down the numbers 0 - 9 in any order and look at the nine 2-digit numbers that you make.

Now score:

1 for a triangular number
2 for a square number
3 for a cube number.

In our example, we had four triangular numbers, three square numbers and one cube number - a score of 13 altogether.

What is the largest score that you can make, and what is the order of the digits that gives that score?

Question 2

Some time ago we were introduced to the world's simplest, yet very pleasing, wooden puzzle. It consists of just two pieces of wood and when you place them together correctly you just know that you have solved the puzzle.

Here is a variation on the puzzle which has four pieces all the same shape that are made by cutting out and gluing the nets on the linked page.

Net for Puzzle Pieces

Challenge
To arrange the four 3D puzzle pieces to make a tetrahedron.

To make the puzzle pieces, you need:

copies of the net made on card (2 sheets)
scissors
ruler
quick-drying glue.

There is a neat method of making the folds easily. Hold a ruler along the lines of the net and, with a point of your scissors, lightly run down the line to score the card. This will make it easy to fold.
Please send a photo of your completed pieces as well as a photo of the pieces arranged to make tetrahedron.

Question 3

The Puzzle
Position the numbers 1 - 12 in this star so that the numbers along each of the six lines of 5 numbers add to the same total.

We've positioned two numbers that belong to a solution in which the total along each line is 33. What does this tell you about the numbers in the triangles that form the points of the star and what is the 33 solution to the puzzle? If you click on the link below you can open up an applet that will help you find the answer.

Star Numbers Applet

There are two ways of solving the puzzle. After finding the first solution, there is an easy method of finding the other one. What is the method and what is the other solution?