*Monday, April 20th, 2020*

The Covid-19 crisis has forced all of us into lockdown. As a matter of fact, it has given a new meaning to the word ** home. **Some people are adapting to it by watching Netflix series, while others are struggling to kill time. In case you are looking for something different on Netflix, I would strongly recommend Paddleton. I believe it teaches us a lot about life and relationships, which a lot of us are anyway learning thanks to Covid-19.

And for those of you, who aren’t Netflix subscribers or just want to get away from the screen sending your friends puzzles are a good idea. You can share this with them by clicking on the button below.

- You need to email your solution before
**19th April (Sunday midnight) to [email protected]** - Best solution will be decided by our faculty team.
- Cash prize of Rs. 500 or free telephonic discussion with Ravi Handa sir about MBA Prep.
- Cash prize of Rs. 500 will be transferred to your PayTM wallet.
- Your solution will be published on the website with your name.
- A quiz is open to everyone above the age of 18.
- You will need to submit an identity proof in case you win a cash prize.

One of my friends, Shobhan has gone to the next level to kill time. He has started giving out cryptic clues to while ordering for essentials on the phone. He lives in a society that has 2000 flats with 10 floors in each building. All buildings are constructed in the exact same fashion with exact same number of flats on each floor. None of the flats in the society have the numbers written on them but they follow a specific pattern. The first digit (or two) is indicative of the floor number whereas the flat numbers on a particular floor are unique 3 digit numbers throughout the entire complex starting from 001. All the flats on a particular floor when arranged in increasing order in Shobhan’s society have their doors open in cardinal directions in alphabetical order.

He has given an order on Dunzo but just to have some fun, he has not mentioned the flat number in the order.

When Billoo, the Dunzo delivery guy, calls him – he tells him the first digit of his flat number and tells him to ask the shopkeeper for the remaining digits. To Nikki, the shopkeeper, Shobhan tells the flat number without telling her the floor or the building number.

Both Billoo and Nikki are horribly confused now. While waiting for Billoo to arrive to pick the stuff up, Nikki calls up Dunzo customer care for all flat numbers in the society that have given an order before from the store because she remembers that Shobhan had ordered from her store before as well. While talking to Dunzo customer care, she makes a list of all previous flat numbers on a piece of paper. Before she could filter the list based upon what she knows, Billoo walks in to pick the stuff up.

When Billoo sees the list, he says – I have no clue where to deliver the goods and I am sure that even you have no idea. Nikki says to Billoo, “Oh – is that so! Well, I have figured it out now. I can tell you where to deliver the goods”. Billoo feels slightly offended and tells her – I don’t need your help. Now even I can go and deliver the goods.

Billoo then picks up the stuff and delivers the goods at Shobhan’s house. Given below is the list:

9089

9123

9171

2108

2198

4123

4157

6108

6157

6171

**Can you tell us Shobhan’s building number and in which direction does his door open? **

Rajat Agarwal rajat.agarwal***@gmail.com

Rahul Jain rahuljain****@gmail.com

Anil Mathew anilmathe***@gmail.com

Harshit Walia emailharshit*****@gmail.com

While there were few other who gave the right answer, the above 4 were the only one who provided a comprehensive correct solution. Please note that the contest is not for just the right answer but the correct explanation of the puzzle. Also, the first correct entry was by Rajat – so once again – being quick isn’t important either.

Special mention and apology to **Ishwar Koki** ishwar****@gmail.com who provided the correct answer and a really good explanation of the puzzle last week but we forgot to mention his name in the list.

**Winner – Anil Mathew** Please email [email protected] with your PayTM number and we will transfer the prize money to you.

The flat number is of the format (ABCD), in which A is the floor number and BCD is the flat number. (A is a single digit as 10 is not an available option in the list of flat numbers provided by Dunzo customer care).

After Shobhan’s calls to Billoo and Nikki,

Billoo knows ‘A’

Nikki is informed of ‘BCD’

Let’s split the conversation that Billoo and Nikki had into multiple parts :

To begin, Billoo looks at the list and says, “I have no clue what the flat number is. And not just that, I’m also sure that you don’t know either.”

The first part of this (I don’t know) indicates that the floor number A repeats in the list and hence Billoo is not sure. This is true for all possible cases based on the list : 2xxx, 9xxx, 4xxx and 6xxx.

The second part of his statement (You don’t know either) indicates that the value of A (which is all he knows) is such that all possibilities of BCD within that set have duplicates across the list. Hence he knows that there’s no way Nikki would have understood which flat it was purely based on the three digit flat number which she was given.

When Nikki hears this, she realises that if Billoo states this with confidence, it cannot be a floor set which has a unique flat number within it. 089 (from 9089) and 198 (from 2198) are unique across the list hence eliminating the floor number sets of ‘9’ and ‘2’. (9089, 9123, 9171,2108,2198)

This leaves us with the 4th and 6th floor sets from the list that have only duplicate flat numbers (BCD).

Further, she goes on to say she’s figured it out.The moment she says this, Billoo also figures out the correct value of BCD. He realises that if BCD was 157 she’d still be confused so both the x157 flat numbers (4157, 6157)are eliminated. This leaves only the numbers 6108, 6171 and 4123.

The fact that Billoo arrives at the correct solution right after knowing that Nikki figured it out proves that the floor number A could have only been 4. If it had been 6, he’d still be confused between the two options 6108 and 6171 and would not know where to deliver.

Since Billoo also understands the flat number it means that 4123 is the flat number because it is the only set left with a single option once ‘157’ is eliminated.

Now for the other part of the problem –

Building number and direction of door. There are 2000 flats with 10 floors each. Hence it’s fair to say there are 200 flats on each floor across the buildings of the entire society.

There are four cardinal directions. When arranged alphabetically they are East, North, South and West.

This order cycles 50 times in 50 buildings until the 200 flats per floor are covered.

I believe it is safe to assume that one floor of a building has 4 flats (and not 8 or another multiple of 4) and hence there are 50 buildings in the society.

Since it’s fairly well established that as there are only 4 flats per floor per building,

Flat 4123 would be on the fourth floor of :

Building Number would be the quotient of flat number (123) when divided by 4, if the remainder is zero. If the remainder of the division by 4 does not yield zero, then quotient + 1 would be the building number. (This is because if a remainder exists, the flat has “spilled over” to the next building )

Hence the building number is Quotient (123/4)+1 = 31 (since there would be a remainder during this division)

Direction :

For the direction the flat opens to, the remainder of the division points us to the answer. Since, flat numbers are arranged in increasing order based on alphabetical order of cardinal directions.

The direction would be

East if BCD mod 4 = 1

North if BCD mod 4 = 2

South if BCD mod 4 = 3

West if BCD mod 4 = 0 (I.e if BCD is divisible by 4)

(mod here means remainder when divided by)

Hence, we conclude that flat 4123 would be located in building 31 with door direction as South.

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