 # Solutions to yesterday's starter

## Alex sent in a fantastic solution:

Here is my solution (I have included all the overlapping squares and rectangles):

Q1.  Squares

• Number of 1x1 squares = 32

• Number of 2x2 squares = 16

• Number of 3x3 squares = 6

• Number of 4x4 squares = 4

I think that there are 56 squares in total.

Q2.  Rectangles

• Number of 1x2 rectangles = 47
• Number of 1x3 rectangles = 30
• Number of 1x4 rectangles = 21
• Number of 1x5 rectangles = 14
• Number of 1x6 rectangles = 6
• Number of 1x7 rectangles = 2
• Number of 2x3 rectangles = 17
• Number of 2x4 rectangles = 10
• Number of 2x5 rectangles = 3
• Number of 3x4 rectangles = 7
• Number of 3x5 rectangles = 2
• Number of 4x5 rectangles = 1

In total there are 170 rectangles.         Alex S  (Hardwick) Y/5

## Here is some super reasoning from Maria:

To find how many squares there are you need to start from a 1x1 square and keep going until there are no more squares small enough to fit in the shape.
1x1:
32
2x2:
16
3x3:
6
4x4:
2
5x5:
0
So I stopped at 5x5 as it's too big to fit in the shape.

## Zoe sent this solution:

Here’s my answer for today’s Maths Challenge.

I found 56 squares and lots  more rectangles too many to count. I got to 70.

From Zoe