Foxide's Maths Puzzles - Brain Teasers (*)

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Foxide's Maths Puzzles - Brain Teasers (*)

Post by Foxide on Fri Jan 22, 2010 10:51 am

This thread will be devoted to Brain Teasers. These are aimed for you to solve over a fair amount of time, but they are not too taxing.

#BT1 (*)

Liam has a house with a staircase. The staircase consists of 12 steps.

Liam can run down the steps 1 or 2 at a time; for example, he could go down the steps in the sequence 1,2,2,1,1,1,2,2, or even 2,2,2,2,2,2, or perhaps 1,1,1,1,1,1,1,1,1,1,1,1. The problem: How many different ways can Liam go down the steps?

EXTENSION (**):

What if Liam's staircase had 100 steps? Or 1000?

Thus, determine a formula for n steps, assuming Liam can still only go down the steps 1 or 2 at a time. Is this more efficient than your previous method? If so, why?

Foxide
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