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Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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Number Sandwiches

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

More Number Sandwiches

Stage: 3 and 4 Challenge Level: Challenge Level:1

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?