Problematics | Shades of cricket and the law of averages - Hindustan Times

Problematics | Shades of cricket and the law of averages

Oct 09, 2023 03:01 PM IST

Can you figure out the game of Inglorious Uncertaintus and create a smart World Cup table? Try this week’s cricket puzzles

It’s been a busy week as far as news is concerned, beginning with the Nobel Prizes and culminating in the assurance of 100+ medals for India in the Asian Games, with the men’s cricket World Cup getting underway in between. By the time you read this, two of these events will have been over (the last Nobel is on Monday), but cricket will be very much on.

Welcome to Problematics!(Shutterstock) PREMIUM
Welcome to Problematics!(Shutterstock)

One of the game’s peculiarities is the way a batter’s average is calculated. Add up their runs and divide the total by the number of times they have been dismissed. Simply put, the denominator is the number of innings played minus the number of times the batter has remained not out.

#Puzzle 59.1
#Puzzle 59.1

#Puzzle 59.1

In one of the World Cup teams, the players were selected through a process that used to be familiar once: First, a longer list of probables based on recent performances, then pruned down after a training camp. Meet Mr Inglorious Uncertaintus, who was not selected among the probables although he had averaged 47 during the domestic season.

Uncertaintus had to admit, however, that his average had been boosted by a significant proportion of not outs among his innings. These included his personal highest. Besides, even with fewer not outs, all the selected probables had averaged over 50.

Our batter had scored three ducks, but no other score was repeated among his innings. “If only I hadn’t scored those three ducks,” Uncertaintus mused. “And if only we had been chasing bigger targets in those innings where I remained not out. I would have scored more runs, because I was batting so well.” If he had scored 5 runs more in each of his not-out innings, he calculated, his average would have been 55 instead of 47.

What was his highest score?

#Puzzle 59.2

#Puzzle 59.2
#Puzzle 59.2

In this table for keeping track of the World Cup results, all 45 matches (pre-knockout) are represented in the cells above the shaded diagonal. You want to grey out the entire chunk below the diagonal. To do so, you use Microsoft Word, whose “Table” feature is handy but has a few limitations.

You can select a row consisting of any number of cells and shade them in one go. This also works for a column of any number of cells. In fact, you can select any chunk of cells in a rectangular arrangement, but cannot include any cell or cells that are “hanging” outside of this rectangle. You can only shade those in a separate batch (or individually).

What is the minimum number of times you would need to press the “shade” button in order to grey out the section below the diagonal above? Start with the grid before any cell has been greyed out.

Mailbox: Last week’s solvers

#Puzzle 58.1
#Puzzle 58.1

#Puzzle 58.1

Hi Kabir,

There will be a total of three copies of Y: one on the front sheet, and two carbon copies. The orientation will be as shown in the illustration.

— Dr Sunita Gupta, Delhi

#Puzzle 58.2
#Puzzle 58.2

#Puzzle 58.2

Dear Kabir,

Two possible solutions are shown in the illustrations. There are more possible transpositions of the same two solutions.

— Group Captain RK Shrivastava (retd), Delhi

Solved both puzzles: Dr Sunita Gupta (Delhi), Gp Capt RK Shrivastava (retd; Delhi), Amit Khanna (Fremont, California), Nagarajan Subramanian (Gurgaon), Anil Khanna (Ghaziabad), Ayush Tandon (Delhi Technical University), Deviprakash Seksaria (Navi Mumbai), Bhasker Mundhra (Ghaziabad), PK Mishra (Delhi), Girish Malhotra (Delhi), Prakash Bhate (Mumbai), Rupali Patwardhan, Sunita & Naresh Dhillon (Gurgaon), Akshay Bakhai (Mumbai), Prof Anshul Kumar (Delhi), Leroy Pereira, Shishir Gupta (Indore), Bhuvi Jain (Delhi), Narendra Prasad, YK Munjal (Delhi), V Anand (Noida), Amardeep Singh (Meerut), Vineet Kumar Dargan (Delhi)

Solved #Puzzle 58.1: Maithili Sharan (Delhi), Sushma Pandhi (Chandigarh), Dr Vivek Jain (Baroda)

Solved #Puzzle 58.2: Rajesh Bansal (Noida), Sakshi & Gaurav Yadav, Yatharth Gahane (Kalyan), Yadvendra Somra (Sonipat), Aryan Pawar, Ashok Kansal, Dr Nakul Makkar (Noida), Vedant Nair, Amar Lal Miglani (Mohali), Anuja Shah (Mumbai), Aryaman Shah (ICT Mumbai), Kanwarjit Singh (Delhi), Nirmit Kohli (Summer Fields International, Kailash Colony), Shri Ram Aggarwal (Delhi)

Problematics will be back next week. Please send in your replies by Friday noon to

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    Puzzles Editor Kabir Firaque is the author of the weekly column Problematics. A journalist for three decades, he also writes about science and mathematics.

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