On the 7th step going down the staircase, I saw Shoumik at the bottom coming up. We met and greeted each other. When I had 4 more steps to go...read on...

### The Riddle

This morning when I went down 7 steps in our staircase, I saw my young friend Shoumik at the foot of the staircase coming up. I continued going down and greeted Shoumik when we met, but I was surprised to see Shoumik at the top when I had still 4 more steps to go. "When I go down 1 step, Shoumik goes up 2 steps," I thought.

How many steps the staircase had? At which point did we meet?

**Recommended time to solve 6 minutes.**

You may feel confused at first. I did. But don't worry. You just have to latch on to the most important clues and ignore the rest.

### Solution to the Going Up and Down a Staircase Riddle

What is the most important information that will lead you to the solution unerringly? I have to discover these crucial clues.

Let me explain taking help of the following flattened out form of the staircase in starting and finishing situations.

The START situation shows relative positions of Me and Shoumik at the start and the FINISH situation shows the relative positions when Shoumik reached the TOP and I am still to go down 4 more steps. Total number of steps is represented by just STEPS.

It is clear, while the "Steps I covered", Shoumik went up the whole way. And the "Steps I covered" is nothing but total number of steps less 11. As Shoumik goes up 2 steps to my going down 1 step, by the time I went down (Total number of steps - 11) steps, Shoumik climbed twice that number of steps which is the total number of STEPS.

A simple equation tell the tale,

Total number of STEPS = 2 x (Total number of STEPS - 11)

Or, Total number of STEPS = 22.

**Solution:** The staircase had 22 steps.

**Let us verify the result** while finding out where exactly Me and Shoumik met on the stairs.

When I reached the 7th step, Shoumik just started coming up. 22-7 = 15 steps separated us. Dividing this gap in the ratio 1 : 2, it is clear, as I went further down 5 more steps Shoumik came up 10 steps from the bottom completing our gap. And *we met on the 10th step from the bottom.*

*All statements in the riddle satisfied and explained as well.*

This seems to be easy because, at the first serious analysis itself I understood that the meeting point is not important. Only important details are in the starting and finishing situations. This is the technique or ability to identify the most important clues in a problem situation ignoring the rest.

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