Copyright © University of Cambridge. All rights reserved.

## 'Even and Odd' printed from http://nrich.maths.org/

This fun problem was about odd and even numbers; it also involved some counting, which is always a good thing! From this specific problem, some general rules began to emerge. This is very useful as these rules can be applied to other problems.

Matthew and Hannah from Stambridge submitted a lovely and clear solution:

Even numbers have two rows of the same number of blocks.

Odd numbers have one extra block in one of the rows.

When you add an odd number of blocks to an even number you get an odd number.

When you add an even number of blocks to an even number you get an even number.

When you add an odd number of blocks to an odd number you get an even number.

Class 4SK from Devonshire also submitted a good solution:

E= Even and O= Odd

E+E=E

O+O=E

O+E=O

three odd numbers added = an odd number

They also explained why this is the case:

An odd number is a number with one left when we pair them up. So if we add 2 odd numbers the two left over can make a pair.

Well done too to children from St Andrews CE Primary School in Oxford whose solution was very similar to Class 4SK's.

Thank you and well done to all those who submitted solutions! If you enjoyed this, why not try the following problem?

If you are only allowed to use $1$s, $3$s and $5$s (but as many of each as you like), can you find all the ways to make $12$ using four numbers? Can you find all the ways to make $13$ using four numbers?