### Homes

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

### Number Squares

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

### Stairs

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

# Baked Bean Cans

##### Age 5 to 7Challenge Level

We had many ideas sent in showing that there were various ways of commenting on the stacking situation. Some sent in pictures or diagrams. Well done all of you!

Joseph from St Martha's School wrote;

Start off with a big number of cans at the bottom and put on less until you run out of cans.

He also sent in this picture.

Rayan from St. James' School sent in the following;

$1$. The best way to stack cans is to put at least $5$ or $4$ cans.
$2$. The supermarkets stack cans like putting $4$ on the bottom, $3$ on the lower middle, $2$ on the upper middle and $1$ above to separate different cans.
$3$. I might safely stack cans up to $10$.
$4$. If you kick it or turn the tray at an angle or pass it to another person on the ground, then the cans will roll.
$5$. Yes it makes a difference between full and empty because full is heavy and empty is light.

Tom and Jack from Stonehenge School said;

We think the best way to stack cans to its highest limit is the traditional method, the method that people use in fairground stalls, what you do is put say: five cans at the bottom, then four on top, then three and so on so on. This is what we think and may not be true.

Their picture is;

Shamim from Ashcroft Techology Academy wrote;

The best way to arrange cans is in a pryamid. Pyramids are the strongest form of support. There are earthquake proof buildings in the shape of a pyramid because the base of the pyramid is big enough to hold the rest of the cans on top. If we were to split a pyramid into squares you can see that for each square above the first line there are two squares below supporting it.