ALL SQUARE 

I want to draw a square in which the perimeter is numerically equal to the area.

Of course, the perimeter will be measured in units of length, for example, centimetres (cm) while the area will be measured in square units, for example, square centimetres (cm2).

What size square will I need to draw?

What about drawing a rectangle that is twice as long as it is wide which still has a perimeter numerically equal to its area?
 

Nim-7     

This is a basic form of the ancient game of Nim.

You will need seven objects, such as counters or blocks. It is a game for two players.

Place the 7 counters in a pile and decide who will go first. (In the next game, the other player will have the first turn.)
Each player takes turns to take away either one or two counters.
The player who takes the last counter wins.

Keep playing until you work out a winning strategy.
Does it matter who has the first turn?
What happens when you start the game with more counters?

NUMBER DETECTIVE 

Calling all detectives! You will need to think creatively, use your reasoning skills and your problem solving strategies to find the mystery number from the list below.

• The number has two digits.
• Both of the digits are even.
• The digit in the tens place is greater that the digit in the ones place.
• The ones digit is not in the three times table.
• The tens digit is not double the ones digit.
• The sum of the two digits is a multiple of five.