Rack Your Brains

 By Anirban Bose

Lead Trainer – Problem Solving, PurpleLeap

The Interview just got Puzzling

Puzzles are an extraordinarily effective and simple way of evaluating what could be called the most important skill for success in an environment of innovation: Problem Solving Skills.

Two things worthy of note here: First, problem solving is not a random gift of destiny; it is a skill and hence can be learnt. Second, mathematical problems are an easy way to determine problem solving ability but it’s still your problem solving skill and not your quantitative aptitude that is being evaluated.

As more and more organizations are converting to the problem solving philosophy and the use of puzzles in interviews, it would do us good to understand what is being tested when you are asked to solve a puzzle.

The simple answer to this would be: APPROACH.

Let us take up a classic puzzle that has been doing the rounds of interviews for quite some time now.

How many ATMs are there in Calcutta (or any other place for that matter)?

This might sound like the 5 Crore question on KBC, but it isn’t. I don’t care about the number of ATMs in a city, so this is an exercise in estimation not in exactness. Your estimate could be way off the mark, but then it’s not the answer but (yes, you guessed it) the APPROACH that matters.

Let us look at 3 approaches to this simple question. Did I say simple? Yes I did, and you’ll see why!

1. The Geographic Approach

Think of an area of 1 sq. Km – how many ATMs would be there. Let’s say 15 ATMs in 1 sq. Km.

Calcutta is roughly 200 sq. km in area, now in any city roughly 40% land area will be unusable, i.e, roads, parks, lakes, golf links, etc. Another 20% would be pure residential layouts and hence will have fewer ATMs (maybe 4/5 in 1 sq. Km).

So our answer is 18 per sq. Km for 100 sq. Km or roughly 1800 ATMs.

2.  The Supply Approach

Let’s say there are 30 banks (that’s a reasonable number) in Calcutta.

The top 10 will want at least 100 ATMs each in 200 sq. Km (1 every 2 sq. Km) – that’s our first 1000 ATMs.

The next 10 banks will want maybe 50 ATMs in the city- that’s our next 500 ATMs.

The last 10 banks would want at least 25 ATMs in the city – that’s our final 250 ATMs.

Total count: 1750 ATMs

3. The Usage Approach

 Calcutta has a population of roughly 5 million – Let’s say 80% have a bank account and rougly 75% of those having a bank account will use an ATM: thus, 3 million.

On average a person uses an ATM 4 times in a month. Therefore the total number of ATM service instances is 12 million per month.

Now an ATM is open 24×7 but is used only 10 hours a day. One ATM service requires at most 3 minutes. 1 ATM services 10 x 20 = 200 instances in 1 day or 200 x 30 = 6000 instances in a month. To service 12 million we would need: 2000 ATMs.

Three different approaches and three different answers (the answer doesn’t really matter) each involving reasonable assumptions and estimations. At the cost of sounding repetitive, let me reiterate: I don’t want an answer; I want to know how you arrived at an answer.

Until next time!

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One comment on “Rack Your Brains

  1. Being someone who is always scared of maths and logical problems, i think this is going to help me a lot. Thanks for making it easy. Looking forward for similar articles. 🙂

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