Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five 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?
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
These diagrams show how you can use rods of lengths 3, 4 and 6 units to measure some lengths:
This set of three rods is special because you can measure all the whole number lengths from 1 to 7 units:
The diagrams above show how to make lengths of 1, 3, 5 and 7.
There are rods for 4 and 6. Can you see how to make 2?
Can you convince yourself you cannot make 8?
Can you find another set of three rods that can be used to measure all the lengths from 1 to 7? What about 1 to 8? 1 to 9? 1 to ...?
How far can you go?