Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Number Sandwiches

*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 to reveal an interactivity that might help you to explore:

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?

Click to reveal another interactivity that might help you to explore:

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.

Printable NRICH Roadshow resource.

## You may also like

### Geoboards

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 7 to 14

Challenge Level

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,

Click to reveal an interactivity that might help you to explore:

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?

Click to reveal another interactivity that might help you to explore:

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

Printable NRICH Roadshow resource.

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