### 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?

### Diagonal Trace

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

# Light the Lights

##### Stage: 2 Challenge Level:

Thomas of QEGS Wakefield identified the rules:

To light the YELLOW light the rule is: < $30$
To light the RED light the rule is: Have an odd tens digit
To light the BLUE light the rule is: Multiple of $5$
To light the GREEN light the rule is: Is odd

Ahmad reasoned well to explain the minimum number which lit up all the lights:

The answer is $15$.
Its tens digit is the smallest, from the allowed, which is $10$. Its unit digit is $5$ ; it is not zero because then it would be even and wouldn't light the green. It is also less than $30$.

Are you both sure that the yellow light only lights up for numbers under $30$?