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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Arranging the Tables

Age 7 to 11
Challenge Level

Arranging the Tables


There are $44$ people coming to a dinner party. There are $15$ square tables that seat 4 people - one at each side - like this:


Or the tables can be joined together to make groups like this:


And so on...

Find a way to seat the $44$ people using all $15$ tables, with no empty places.


Why do this problem?

This is quite a fun activity to do both numerically and practically using something like multilink to represent the tables. It gives an opportunity for pupils to explore a real situation and see the mathematics contained in it, and what can be investigated further.

Possible approach

Pupils should be encouraged to choose what practical bits and pieces might help them to find solutions. The solutions would probably be best recorded somehow. Again, pupils should be encouraged to find good ways of recording which suit them. Some might draw pictures, some may use sketches and some may just use numbers. (Some examples can be found on the sheet linked to the extension below.)

In a plenary, as well as focusing on solutions, you could draw attention to the different ways children have used to record their work.

Key questions

What do you see here?
How are you getting to your answer?

Possible extension

See this sheet for suggestions.

Possible support

Using some resources to show the situations practically would help some pupils.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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NRICH is part of the family of activities in the Millennium Mathematics Project.