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Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Summing Consecutive 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?

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Big Powers

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You Can't Make an Omelette...

Stage: 3 and 4

This resource is part of "Freedom and Constraints"

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 se
cond 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?

Perhaps drop the first egg from the 5th floor and if it breaks, use the second egg to test floors 1 to 4.
And if it doesn't break...

Can you come up with a strategy using both eggs to minimise the number of trials you'd have to do in the worst case scenario?

What other interesting mathematical questions can you think of to explore next?
We have thought of some possibilities:
Can you devise the most efficient strategy for finding the highest floor from which you can drop the egg safely?

What if there were more floors?
What if you had more eggs?

We'd love you to share the questions you've come up with. Tell us also how you got started and any conclusions you have arrived at. 
Send us your thoughts; we'll be publishing a selection.