### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

# Number Sandwiches

##### Age 7 to 14 Challenge Level:

You may wish to print off two sets of digit cards to cut out and play with.

In this arrangement there is one number sandwiched between the "1" cards, two numbers sandwiched between the "2" cards, but only one number sandwich between the "3" cards.

Is it possible to make a complete sandwich with one number between the "1" cards, two numbers between the "2" cards, and three numbers between the "3" cards?

Click and drag the leftmost number in each pair. The number on the right will move with it.

I wonder if there is more than one way to arrange the numbers...

Can you make a complete sandwich with 1, 1, 2, 2, 3, 3, 4, 4?

I wonder if there is more than one way to arrange the numbers this time...

It is also possible to make a sandwich using 1s, 2s, 3s, 4s, 5s, 6s and 7s.
Can you find an arrangement?

Click below to see one possible solution. Is yours the same?

I wonder how many different solutions there are...

If you have any problems using the interactivities you can use the versions on the GeoGebra website: Sandwiches Interactivity.

If you enjoyed this problem, you might like to try More Number Sandwiches.