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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# More Number Sandwiches

In Number Sandwiches you may have made sandwiches with the numbers 1 to 3, 1 to 4 and 1 to 7.

Can you use the interactivity below to make sandwiches with the numbers 1 to 5? Or 1 to 6?

Sometimes it is difficult to tell whether a task is impossible, or just very difficult!

Can you convince yourself that it is impossible to make sandwiches with the numbers 1 to 5, and 1 to 6?

Click below to reveal some questions that might help you to explain what is happening:

In a "7-sandwich", how many red squares are covered and how many blue squares are covered?

If it were possible to make a "6-sandwich", how many red squares and how many blue squares would be covered?

Click below to reveal some more questions that might help you develop your thinking further:

If you place a 1 on a blue square, on which colour will you place the other 1?

If you place a 2 on a blue square, on which colour will you place the other 2?

If you place a 3 on a blue square, on which colour will you place the other 3?...

**In general, what can you say about the colours on which you place pairs of numbers?**

When you try to make a sandwich with the numbers from 1 to 5, or from 1 to 6, what goes wrong?

Which other sandwiches are impossible? How can you be sure?

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Age 11 to 16

Challenge Level

In Number Sandwiches you may have made sandwiches with the numbers 1 to 3, 1 to 4 and 1 to 7.

Can you use the interactivity below to make sandwiches with the numbers 1 to 5? Or 1 to 6?

Sometimes it is difficult to tell whether a task is impossible, or just very difficult!

Can you convince yourself that it is impossible to make sandwiches with the numbers 1 to 5, and 1 to 6?

Click below to reveal some questions that might help you to explain what is happening:

In a "7-sandwich", how many red squares are covered and how many blue squares are covered?

If it were possible to make a "6-sandwich", how many red squares and how many blue squares would be covered?

Click below to reveal some more questions that might help you develop your thinking further:

If you place a 1 on a blue square, on which colour will you place the other 1?

If you place a 2 on a blue square, on which colour will you place the other 2?

If you place a 3 on a blue square, on which colour will you place the other 3?...

When you try to make a sandwich with the numbers from 1 to 5, or from 1 to 6, what goes wrong?

Which other sandwiches are impossible? How can you be sure?