Question 1

When our twins, Eddie and Richard, were small, we made a jumping game for them out of some old pavers that we picked up at the dump. We made the rules of the jumping game as easy as possible and here they are:

1. You must jump into a paver that is next to the one you are in.

2. You must not jump into a paver more than once.

3. You must add up your score as you jump from Start to Finish.

Then the twins added their own rules.

4. You must make the same score as the other person.

5. You must not follow the same path as the other person.

6. You lose if you make a score that can only be made in one way.

Questions

1. What is the score made by the line followed by Eddie?

2. What different routes could Richard take to make the same score?

3 .What are the losing scores, according to Rule 6?

Question 2

Imagine that there are lots of cakes set out in 2 rows and any number of columns, as in the diagram below.

Two players who we could call Vertica and Horizo are about to have a cake eating competition. Being the girl, Vertica goes first and she can select which vertical row to eat the cakes in. Here's the position if Vertica selects Column 4.

Then it's Horizo's turn, and he now has four horizontal rows he can choose from. Here's the position if he chooses the top left row.

They continue eating from the vertical and horizontal rows until one player eats the last piece of cake and is declared the winner.

Question
What should Vertica's strategy be if she is to beat Horizo every time? Can you please advise her.

There is an applet that you can use to give you ideas. It allows you to have one row or two and you can vary the number of columns. Click on the link below to launch the applet.

EatCakesJunior

We recommend that you start with just one row of cakes as it is easier to work out what happens in that situation.

Question 3

Ann has been making a number bracelet. She has used five silver rods that join ten bead holders and she has also made a set of ten beads numbered 1 to 10. Her idea is that she can change the numbers in the bead holders to make different bracelets, but she is wondering if it would be possible to make the numbers along each silver rod add to the same total. She thinks that would make a naturally mathematical bracelet, but she doesn't know if one can be made.

Question 1
Please tell Ann if you can make an arrangement of the beads 1 - 10 that will make a naturally mathematical bracelet.

Question 2
Do you think there might be other arrangements of the beads that will make different totals? Ann would really like to know what they are if you can find them.

Please … Ann needs an explanation of the strategy that you used to find the naturally mathematical arrangements, as she would like to try your strategy on the next bracelet she plans, where there will be six silver rods instead of five.