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If there are only a handful of objects, then you can count them with a moment's thought, but the techniques of combinatorics can extend to quickly and efficiently tabulating astronomical quantities. See more

What is the next number in this sequence?

\[0, 1, 3, 6, 10, 15...\]

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How many corners does a *hypercube* (a 4-dimensional cube) have?

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How many line-segments are there in the 4th image of this growing tree sequence?

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What is the sum of the first 13 positive odd numbers?

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The sizes of the first 9 squares that make this spiral are:

\(1, 1, 2, 3, 5, 8, 13, 21, 34... \)

How big is the 10th square added to the spiral?

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