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

Summing Consecutive Numbers

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

Number Sandwiches

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

What Does it All Add up To?

Age 11 to 18
Challenge Level


Why do this problem?

This problem, along with the rest of the problems in the Proof for All (st)ages feature, provides an excellent context for observing, conjecturing and thinking about proof, and for appreciating the power of algebra.


Possible approach

This problem featured in an NRICH Secondary webinar in January 2022.

These printable cards for sorting may be useful: 
What Does it All Add Up To Proof Sort

Key question

Is there a way to represent the sum of four consecutive numbers that will help to explain the patterns you noticed?


Possible support

Encourage students to work in pairs on the proof sorting exercise.
Before embarking on this problem, students could take a look at Three Neighbours.


    Possible extension

    Students could be encouraged to work on the rest of the problems in the Proof for All (st)ages feature.