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.
Imagine you work for a factory that makes egg-shaped ornaments. On the packaging, you need to tell customers how high the eggs can be safely dropped from, without them breaking!
The factory manager gives you an egg to test from each floor of a 100 storey building.
You will need to drop it from the first floor, and if it doesn't break, go up to the second floor, and if it doesn't break, go up to the third floor...
In the worst case scenario, you might have to do 100 tests to find out where it breaks!
"This could take ages! Can I have an extra egg to make life a bit easier?"
"Yes, here you are."
How will you use the extra egg so that you don't need to do so many trials?