A monk has a very specific ritual for climbing up the steps to the temple.

First he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears a bird singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes him 9 paces. How many steps are there?

There are 49 steps.

He hears the bird singing on step 33. He picks up the pebble on the 21st step and tosses it on the 22nd step. The remaining 27 steps are taken three at a time which is 9 paces.

Here is one way to solve it. Since there _is_ a middle step, the number of steps is odd. So the number of steps has the form 2N+1, where N is a number we have to figure out. Let's number the steps starting from the bottom, so the first step is 1, then the second is 2, and so on. The middle step is then the (N+1)st step, since it has N steps below it and N steps above it. Now let's just follow the monk with this notation in mind. We can of course ignore everything he does besides taking steps, although I guess that information makes the problem more picturesque.

He goes to the middle step: that's step N + 1.

He climes 8 more: going to step (N + 1) + 8 = N + 9.

He walks down 12 steps: getting him to step (N + 9) - 12 = N - 3.

He takes one step up: so he's at (N - 3) + 1 = N - 2.

Nine paces of three steps each gets him to the top. In nine three-step paces we travel 9*3 = 27 steps. Since this gets us to the top step, which is step 2N + 1, we're told that

(his current position) + 27 = (the top step) = 2N + 1.

Since his current position was N - 2 we find that

N - 2 + 27 = 2N + 1.

Moving all the numbers to the left hand side and all the Ns to the right and simplifying we find that 24 = N. So there are 2N + 1 = 48 + 1 = 49 steps.