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Can you work out the equations of the trig graphs I used to make my pattern?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

This problem challenges you to find cubic equations which satisfy different conditions.

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?