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Puzzle of The Week – Best Solution Wins Cash Prize – Indian cricket team participated – Updated with Solution

Monday, April 6th, 2020

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Puzzle of The Week – Rules and Prize

• You need to email your solution before 5th 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.

Puzzle of The Week – Question

Indian cricket team participated with five opening batsmen (Kannur, Shikhar, Rohit, Prithvi, and Mayank) in the 2020 ICC T20 tournament. In the league stage, a different pair opened the batting for India in every match. There were a total of five century partnerships for the first wicket against Australia, England, New Zealand, Pakistan, Sri Lanka. Every batsman was a part of two century partnerships.

Every century partnership involved Mayank, Kannur, or Shikhar but there was no batsman common in the century stands against Australia and Sri Lanka.

Kannur got out after scoring 7 against Australia in the third over he played.

Mayank was involved in the century stand against England.

One batsman was involved in the century stand against both England and Pakistan.

The batsman who shared a century stand with Shikhar was also involved in the century stand against New Zealand.

Rohit got out on the first ball when he opened with Kannur.

India qualified for the semifinals because of the phenomenal performance by Prithvi and Mayank in the last match where they posted the highest first wicket partnership of the tournament.

In the semifinals, India is supposed to go battle it out with New Zealand. The coach Shastri and the captain Virat think it would be a good idea to open with the pair that hit the century against New Zealand in the league match.

So, who do they select to open in the Semi Finals?

Puzzle of The Week – Solution and Winner

Answer – Kannur and Prithvi

There are 5 opening batsmen, and since different pair opened batting for India in every league match we know that total number of league match India played is  and equivalent possible opening pairs to consider which are –

{ Note – We will denote a pair by the player’s first letter in parentheses separated by symbol + like (K+S) denotes the opening pair of Kannur and Shikhar. Also note that, this pairing is combinatorial and hence order of player name is irrelevant, i..e + is commutative → K+S and S+K denotes same pair. }

Total possible pairs	Exclusions striked out
(K+S) , (K+R) , (K+P) , (K+M)	(K+S) , (K+R) , (K+P) , (K+M)
(S+R) , (S+P) , (S+M)	(S+R) , (S+P) , ( S+M)
(R+P) , (R+M)	 (R+P) , (R+M)
(M+P)	(M+P)

First, we select 5 pairs from this group who scored centuries against given teams.

• Since, Rohit got out on first ball when opened with Kannur implying they are not century scoring pairs we can exclude (K+R).
• Every century partnership include Mayank,Kannur or Shikhar implying we can exclude paris which do not have M or K or S in them → (R+P)
• Since every batsman is part of 2 partnerships, R’s remaining group must be included since 2/4 are excluded just above → (R+S) and (R+M) must be there
• Mayank and Prithvi scored highest partnership in the last league match → (M+P) is included. Further implying that other remaining pairs with M excluded → (S+M) (K+M). Remaining only 2 pairs having K must be there and hence (S+P) not

So we have 5 pairs –

(K+S) , (K+P) , (S+R), (R+M), (M+P)

 Now Kannur got out after scoring 7 in the third over against Australia which implies that it is a match where Kannur did not open and century partnership was not done. { A century partnership with score of 93* and 7 to opening batsman, assuming rationality since 4 balls are minimum required for getting out at 7, remaining balls can not be used to score 93*}.

Anyway taking this case, i.e. (K+S) or (K+P) did score a century opening partnership against Australia, we ended with no solution with given constraints. So these pairs can be removed from Australia century stands. So possible australia stand → (S+R) (R+M) (M+P)

Since Mayank was involved against England century stand so 2 choices are there → (M+P) or (M+R).

Only batsman to share a century pair with Shikar is R or K so possible choices for the New zealand stand are → (K+P) , (R+M) . Since Shikar is obviously not part of it (no repetition).

Pakistan and Englands stand have 1 batsman common ( i.e. M or R or P), so it cannot be (K+S)

So Srilanka stand must be → (K+S)

 Since Srilanka stand and Australia stand do not share any batsman, (R+S) is not an Australia stand.

We have now choices :

Australia	England	Pakistan	New Zealand	Sri lanka
(R+M) (M+P)	(M+P) (M+R)	(K+P) (R+S) (R+M)	(K+P) (R+M)	(K+S)

Clearly (R+S) is the opening stand against Pakistan. (as no other location in table)

Australia	England	Pakistan	New Zealand	Sri lanka
(R+M) (M+P)	(M+P) (M+R)	(R+S)	(K+P) ( R+M)	(K+S)

Clearly (K+P) is the opening stand against NewZealand(as no other location in table) And

Hence the answer → Kunnar and Prithvi.

Further (M+P) can not be a pair against England, as they do not have 1 batsman in common with Pakistan. Pair against England and Australia turns to be (M+R) and (M+P) respectively. So pairs are :-

Australia	England	Pakistan	New Zealand	Sri lanka
 (R+M) (M+P)	 (M+P) (M+R)	(R+S)	(K+P)	(K+S)

 

Puzzle of The Week – Winner

Garima Yadav – garimaya*****@yahoo.in

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