Problematics | Batting failures
How many runs did Sunny, Don, Viv and Garfield score in this match among elders? The information is limited, but the puzzle can be solved.
When we talk about puzzling as an interactive activity between setters and solvers, we recognise the pioneers in the field as Henry Ernest Dudeney, Sam Loyd and Lewis Carroll, their work spanning the 19th and 20th centuries. The one who really popularised these puzzles among a newer generation, besides introducing the work of many other old and new puzzlers including his own, was Martin Gardner, the late American author and puzzler.
It would be pointless to reproduce Gardner’s puzzles in their original form because the answers are so widely accessible. The way out, of course, is the same as that for many other puzzles in Problematics: an adaptation. The following puzzle is essentially Gardner’s and uses the same numbers; I have only embellished it by wrapping it into a different situation.
#Puzzle 104.1
A group of legendary players, now retired, are playing a T20 match. For ease of identification, let us call the top four batters of one side Sunny Pastures, Don Corleone, Viv Leigh and Garfield the Cat. We catch up with them after their side has completed their innings and three fans are discussing their poor performance. Only one of them has watched the innings and is briefing the other two.
Fan #1: All four of the superstars have performed miserably. In fact, they have contributed less than 18 runs put together.
Fan #2: Has any of them scored a duck?
Fan #1: No. Although that hardly matters, each one has opened his account. In fact, no two batters have the same score. Sunny has the top score among the four, Don has more runs than Viv, and Garfield has the lowest score.
Fan #3: Let us try to work out the individual scores without consulting the scoreboard. What more information can you share?
Fan #1: The product of these four individual scores is the same as the team total.
Fan #2: We still don’t have enough information to solve the puzzle. Just one more question. Is Garfield’s score more than 1?
Fan #1: ___ (A yes or no answer, withheld from readers)
Fans #2 & #3: Got it now!
What are the individual scores of the four grand old men?
#Puzzle 104.2
x/3 + x²/2 + x³/6 = 1
Is there enough information here to find or rule out an non-integer solution for x?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 103.1
Hi Kabir,
As the minimum quantities are to be added to maintain the prescribed ratio in the final solution, the mathematician keeps the quantity of the first solution (AUB #121) the same since it has the lowest number of drops. He then calculates the quantities of other solutions and salt to be added to maintain the same ratio of 24/18 = 4/3 of the original recipe for each ingredient. The quantities are shown in the table.
— Anil Khanna, Ghaziabad
#Puzzle 103.2
Hi Kabir,
Let’s say, the number of pairs of shoes bought = x. Cost price of each pair = ₹60000/x, number of pairs sold = (x – 15), and selling price of each pair = ₹54000/(x – 15). Since the profit is ₹100 per pair, we have
54000/(x – 15) = 60000/x + 100
Solving, we get
x² + 45x – 9000 = 0
or, x = –120, 75. Rejecting the negative root, x = 75
Number of pairs of shoes bought = 75 @ ₹800 each
Number of pairs sold = 60 @ ₹900 each
— Dr Sunita Gupta, Delhi
A couple of the replies received for #Puzzle 103.1 keeps the quantity of salt untouched while adding extra amounts to all solutions. While this is not the smartest solution (it requires more quantities to be added), I am still including these in the list of correct answers.
Solved both puzzles: Anil Khanna (Ghaziabad), Dr Sunita Gupta (Delhi), YK Munjal (Delhi), Akshay Bakhai (Mumbai), Sanjay Gupta (Delhi), Professor Anshul Kumar (Delhi), Sampath Kumar V (Coimbatore), Sanjay S (Coimbatore), Shri Ram Aggarwal (Delhi), Ajay Ashok (Delhi), Aditya Krishnan (Coimbatore), Shishir Gupta (Indore), Harshit Arora (IIT Delhi), Yadvendra Somra (Sonipat).
Solved #Puzzle 103.1: Raghunathan Ravindranathan (Coimbatore)
Solved #Puzzle 103.1: Sundarraj C (Bengaluru), Jaikumar Inder Bhatia & Disha Bhatia (Ulhasnagar, Thane)