Don’s ten
Aditya Rishi

Read Euler: he is our master in everything. - Pierre-Simon de Laplace (1749-1827)

AFTER beating Donald Bradman for the award, Leonhard Euler told journalists why he was so successful: "I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand."

After this, Don was asked to pick ten members for his all-star team. Don said cricketers who played by the book were written about, but those who produced shots that were out of this world became stars. His dream team will have both.

Nitin Khanna replaces Tendulkar in the team. Check out his square cut (solution to Euler’s problem: to look at 18530, 65570 and 45986 and find the fourth number that will complete his set so that any two added together form a perfect square): "Let the numbers be:

a 18530

b 65570

c 45986

x number to be found

b-a= 47040; b-c= 19584; (b-a)-(b-c) = 27456, which means that difference of difference of numbers is decreasing by 27456 each time.

Therefore:

(c-x)-(c-b) = 27456

c-b= -19584

c-x= 45986-x

Therefore: 65570-x = 27456

x = 65570-27456

x = 38114, the number Euler wants."

Vijayesh Narayan Singh, a third-year student of B.Sc (honours school) Mathematics in Panjab University, Chandigarh, replaces "Mr Dependable" Rahul Dravid in the team for his ability to play long innings. Though technically correct, he takes a lot of deliveries to get set and reach the target.

"18530+65570-45986 =38114; sqrt(18530+38114)=238; sqrt(65570+38114)=322; sqrt(45986+38114)=290; so, solution is 38114," says Arun Shah. Effective shot, but dangerous. He’ll bat lower down.

"Let the fourth number be x; 18530 + 65570 = 45986 + x; Thus, 84100 = 45986 + x; Thus, x = 84100 - 45986 =38114. The number 38114 fulfills all the conditions. 45986 + 38114 = 84100, which is the square of 290. Similarly, 18530 + 38114 = 56644 which is the square of 238; 65570 + 38114 = 103684 which is the square of 322; 65570 + 45986 = 111556 which is the square of 334," say Geeta and Rahul Aneja from Karnal.

"The sum of 65570 and 18530 is 84100, which is a perfect square, and if we subtract 45986 the balance is 38114. This must be the number which when added to 45986 becomes a perfect square. This was just by luck. When I added this number to 18530 and 65570, the sum in both cases was a perfect square," says Dr Tarsem Lal from Khanna. Geeta Aneja, Rahul and Dr Tarsem lend youth and experience to the middle order.

To fox opposition with bouncers and googlies, Don has included Geetika Gupta (Thapar, Patiala), Arshdeep Singh (Jalandhar), Ajit Partap Singh (Ludhiana) and Ravneet Kotwal (Jalandhar) in the team. They play copybook cricket and their copybook is in their computers. An announcement: Sir Don has just announced his retirement. The team will now be led by Leonhard Euler. (Write at The Tribune or adityarishi99@yahoo.co.in)