## Understanding the Two-Way Movement in a Staircase Riddle: Use Core Insight

This staircase riddle challenges your problem-solving skills by combining logical thinking with the concept of two-way movement on a staircase.

### The Two-Way Movement in a Staircase 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 comes up 2 steps," I thought.

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

**Recommended time to solve 6 minutes.**

Though it seems tricky at first, with the right approach, it's an exciting challenge! But, don't worry. You just have to **focus on the most essential ideas and ignore the rest.**

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

What is the most important information that will lead you straight to the solution? I had to discover these crucial clues. And I did it quickly.

Starting and finishing situations of Me and Shoumik with all the important details hold the most important clues for solving this puzzle with ease.

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

**The START situation shows:** When I was on the 7th step, Shoumik was just at the point of coming up from the foot of the staircase.

**The FINISH situation shows:** Me at a point in the staircase still to cover 4 steps to reach the bottom while Shoumik had already reached the top.

**Key insight:** While the "Steps I covered", Shoumik went the whole way up the staircase.

The "Steps I covered" is nothing but the total number of steps less 11. As Shoumik comes 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 tells 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.

#### Second challenge: Where did we meet?

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

**Our separation at the starting situation:** When I reached the 7th step, Shoumik just started coming up. (22 - 7) = **15 steps separated us.**

Since Shoumik climbs up twice as fast, when I covered 5 more steps, Shoumik would have climbed 10 steps, and we would meet exactly where the 15-step gap closes, on the 10th step from the bottom.

**Answer to the second challenge:** We met on the 10th step from the bottom.

### For the Math-inclined: Solution Using Ratio Concept

Since Shoumik climbs twice as fast as I go down, the ratio of our relative speed is 2 : 1 (2 for Shoumik, 1 for me). Divide the gap of 15 steps in a ratio of 2 : 1 and you will get: *Shoumik climbed 10 steps while I went down 5 steps, closing the gap of 15 steps between us.*

### End words

This puzzle solution 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, while ignoring the rest. This is the **Core Insight Method** that not only helps in solving puzzles but can apply to many problem-solving situation in life.

### Did you solve it within 6 minutes?

If you could solve it within 6 minutes, share your solution through mail at * myrequest@suresolv.com (link sends e-mail).* If your approach is great with a fresh angle, I will include it here as a further update.

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**Matchstick puzzles**You may also look at the full collection of puzzles at one place in the **Challenging brain teasers with solutions: Long list.**

*Enjoy puzzle solving while learning problem solving techniques.*