Number Detective

Follow the clues to find the mystery number.

Red Even

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Prime Magic

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Magic Vs

Stage: 2 Challenge Level:

Place each of the numbers $1$ to $5$ in the V shape below so that the two arms of the V have the same total.

How many different possibilities are there?
What do you notice about all the solutions you find?

Can you explain what you see?

Can you convince someone that you have all the solutions?

What happens if we use the numbers from $2$ to $6$? From $12$ to $16$? From $37$ to $41$? From $103$ to $107$?

What can you discover about a V that has arms of length $4$ using the numbers $1-7$?