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'The Mathemagician's Seven Spells' printed from http://nrich.maths.org/

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1. "It's doubling!" whispered Anna.
2. "I've seen numbers like that on a calendar," said David.
3. "It's a bit like the doubling going backwards," thought Anna.
4. "Triangular numbers!" declared David.
5. "It might help to look at the gaps between the numbers," suggested Anna.
6. "Cubes!" announced David.
7. "Wow!" gasped Anna, "How can we do that one?"
"It's like the one where you looked at the gaps - but here it's the gaps between the gaps," answered David.