Eddington's Cricket Puzzle
The name of famous British astrophysicist Arthur Eddington was first introduced to me at the age of 10 in my school class VI. We studied a text book titled "Pancha Maha Pratibhakal" (Five Great Talented Men) about the lives of 5 Indian scientists (Prafulla Chandra Ray, C V Raman, Srinivasa Ramanujan. J C Bose and Subrahmanyan Chandrasekhar). Eddington was the antagonist, in the way it was portrayed in the biography of S Chandrasekhar contained in the aforementioned text book.
I have to say a little about theoretical physicist, Subrahmanyan Chandrasekhar. Chandra (short name for Chandrasekhar, and the usual way he was addressed) was a prodigy in mathematics and physics. Astounding scientific talent abounded in his family. His maternal uncle was the Nobel Laureate C.V. Raman. At the age of 18 as an undergraduate at the Presidency College Madras, Chandra wrote a paper which developed new applications of Fermi Statistics. As a 19 year old from British India, Chandrasekhar worked out with the help of a handful of texts at his disposal on his long ship journey to Britain, the first definitive study of evolution of stars. He arrived at the surprising conclusion that 'The life history of a star of small mass must be essentially different from the life history of a star with large mass. For a star of small mass, natural white dwarf stage is an initial step towards extinction. A star of large mass cannot pass into the white dwarf stage and one is left speculating on other possibilities'. He was prudent enough not to publicly state or publish his explorations on the 'other possibilities' (mathematical explorations of relativity theory was in its infancy in 1920's, with the golden age of cosmology almost 3 decades away). Given his formidable mathematical talent, it is quite conceivable that Chandra would have sketched a derivation or at least speculated the inevitability of singularity at the end of life for a star with mass few times the Sun.
I have to say a little about theoretical physicist, Subrahmanyan Chandrasekhar. Chandra (short name for Chandrasekhar, and the usual way he was addressed) was a prodigy in mathematics and physics. Astounding scientific talent abounded in his family. His maternal uncle was the Nobel Laureate C.V. Raman. At the age of 18 as an undergraduate at the Presidency College Madras, Chandra wrote a paper which developed new applications of Fermi Statistics. As a 19 year old from British India, Chandrasekhar worked out with the help of a handful of texts at his disposal on his long ship journey to Britain, the first definitive study of evolution of stars. He arrived at the surprising conclusion that 'The life history of a star of small mass must be essentially different from the life history of a star with large mass. For a star of small mass, natural white dwarf stage is an initial step towards extinction. A star of large mass cannot pass into the white dwarf stage and one is left speculating on other possibilities'. He was prudent enough not to publicly state or publish his explorations on the 'other possibilities' (mathematical explorations of relativity theory was in its infancy in 1920's, with the golden age of cosmology almost 3 decades away). Given his formidable mathematical talent, it is quite conceivable that Chandra would have sketched a derivation or at least speculated the inevitability of singularity at the end of life for a star with mass few times the Sun.
Chandrasekhar on and off worked on his theory about White Dwarfs and after finishing his PhD at the Cambridge University (where Arthur Eddington was professor and the leading authority on stellar evolution), Chandra finally developed an exact theory of star collapse of stars with mass few times that of Sun, and presented the results at the proceedings of Royal Astronomical Society in 1935. This paper discussion was immediately followed by Eddington's paper titled "Relative Degeneracy" which roundly disputed Chandrasekhar's work on White Dwarfs as physically unrealistic. The strangest aspect of this rebuttal paper by Eddington, was the way in which he continuously monitored progress of Chandra's theoretical development of stellar mass limits. The pre-planned denouncement of Chandra's work on the same day of presentation in retrospect, can only been seen as "sheer mean spirited duplicity".
Some speculate that racial prejudice was to be one of the reasons for such an act. Other scholars state that Chandra's mathematical derivation left grounds for physical speculation on the basis of Quantum Mechanics theory (then in its infancy - but after the triumphant derivation of Electron equation by P.A.M. Dirac, and Von Neumann's work on the mathematical foundations of Quantum Mechanics, the field was on much firmer theoretical grounds) which may have (based on theoretical speculations at the time) precluded such a fate for a massive star. Whatever be the reason, Chandra was bitterly disappointed that none of the "Giants of Science" publicly supported his theory of stellar collapse, but only privately confirmed the correctness of his research. Eddington's intransigence to accept revolutionary extension to the theory of stellar evolution may have triggered Chandrasekhar's decision to leave England. It is ironic that Chandrasekhar received the Noble prize in Physics in 1983 precisely for his work on stellar evolution while Eddington, given his reputation, never won a Nobel prize in his storied scientific career.
I have come across one of Chandrasekhar's earlier papers about Brownian Motion and Stochastic Processes and its application to solution of problems in Stellar Physics, the only paper of his that I could read and understand even a tiny bit. I was wonder struck by the mathematical prowess and clarity of thoughts with deep physical insights and the authoritative lucid mode of presentation of as fundamental a topic as the study of stochastic processes, displayed in abundance in the paper. Chandrasekhar is also known to change his fields of study every decade or so. His modus operandi was roughly 1) Select a new field of study - mostly a disorganized field with a need for theoretical unification 2) Make a literature survey and the current state of the development 3) Study the main problems and make fundamental contributions extending/unifying the theory 4) Write an authoritative book which extends and summarizes all of what is known and developed about the field and then go back to step 1. Possible only for a scientist possessing such a monster mind. He was a true scholar indeed.
After reading more about Eddington, I can now say that with his wealth of results and supreme intellect, he could have been a sure shot Nobel prize winner. (Eddington may have died relatively young for award of Nobel prize). He was also noted for his complete mastery of Relativity Theory and his philosophical speculations about science. He is also the scientist who reportedly replied thus when told by a journalist that only 3 people in the world understood general theory of relativity. His retort was "Who is the third one?"
I have come across one of Chandrasekhar's earlier papers about Brownian Motion and Stochastic Processes and its application to solution of problems in Stellar Physics, the only paper of his that I could read and understand even a tiny bit. I was wonder struck by the mathematical prowess and clarity of thoughts with deep physical insights and the authoritative lucid mode of presentation of as fundamental a topic as the study of stochastic processes, displayed in abundance in the paper. Chandrasekhar is also known to change his fields of study every decade or so. His modus operandi was roughly 1) Select a new field of study - mostly a disorganized field with a need for theoretical unification 2) Make a literature survey and the current state of the development 3) Study the main problems and make fundamental contributions extending/unifying the theory 4) Write an authoritative book which extends and summarizes all of what is known and developed about the field and then go back to step 1. Possible only for a scientist possessing such a monster mind. He was a true scholar indeed.
After reading more about Eddington, I can now say that with his wealth of results and supreme intellect, he could have been a sure shot Nobel prize winner. (Eddington may have died relatively young for award of Nobel prize). He was also noted for his complete mastery of Relativity Theory and his philosophical speculations about science. He is also the scientist who reportedly replied thus when told by a journalist that only 3 people in the world understood general theory of relativity. His retort was "Who is the third one?"
Little did I know that Arthur Eddington was also a puzzle enthusiast and some of his puzzles were genuine brain twisters. One of the best puzzles I have ever come across is Eddington's Cricket Puzzle.
First of all the puzzle is as follows.
THE PUZZLE
An Imaginary Scoreboard
Atkins 6
Bodkins 8
Dawkins 6
Hawkins 6
Jenkins 5
Larkins 4
Meakins 7
Perkins 11
Simkins 6
Tomkins 0
Willkins 1
Extras 0
Total 60
BOWLING
Pitchwell: 12.1-2-14-8
Speedwell: 6-0-15-1
Tosswell: 7-5-31-1
CLUES:
1. The Batsmen have scored only in singles and 4s.
2. All of them were clean bowled. No one was caught or run out. There were no no balls or 'short' runs.
3. Speedwell and Tosswell bowled 6 and 7 overs respectively at a stretch.
4. Pitchwell opened the bowling, with Speedwell coming in at the other end for the next over.
5. The overs were of 6 balls each.
QUESTIONS:
1. Which bowler dismissed which batsmen?
2. Who was not out?
3. What were the Fall of Wickets?
An Imaginary Scoreboard
Atkins 6
Bodkins 8
Dawkins 6
Hawkins 6
Jenkins 5
Larkins 4
Meakins 7
Perkins 11
Simkins 6
Tomkins 0
Willkins 1
Extras 0
Total 60
BOWLING
Pitchwell: 12.1-2-14-8
Speedwell: 6-0-15-1
Tosswell: 7-5-31-1
CLUES:
1. The Batsmen have scored only in singles and 4s.
2. All of them were clean bowled. No one was caught or run out. There were no no balls or 'short' runs.
3. Speedwell and Tosswell bowled 6 and 7 overs respectively at a stretch.
4. Pitchwell opened the bowling, with Speedwell coming in at the other end for the next over.
5. The overs were of 6 balls each.
QUESTIONS:
1. Which bowler dismissed which batsmen?
2. Who was not out?
3. What were the Fall of Wickets?
I love solving good puzzle, the more logical, the better it is to me. I was thinking on solving cricket puzzle for some days, once I even sketched the solution but some of my answers were not logically sound. My theory was that, this being a beautiful jigsaw of logic, its derivation should occur naturally.
Later I got enough time to solve it and here is my solution.
I have'nt seen any other detailed solutions on the internet and would not want to spoil the genuine thrill of solving this beautiful puzzle.
Hence I will only provide a brief sketch of solution as follows.
I sketched my solution thus.
Step 1 - Order of bowling can be deduced.
Step 2- Tosswell's bowling analysis can be found.
Step 3 - We will get some deductions once the run flurry in Mr Tosswell's overs are taken to its logical conclusion.
Step 4 - From the deduction in the above step we can work out the runs analysis of each of the batsmen.
Step 5 - We can then workout the fall of wickets, who got whom out and the last man standing with straight forward reasoning.
Step 1 - Order of bowling can be deduced.
Step 2- Tosswell's bowling analysis can be found.
Step 3 - We will get some deductions once the run flurry in Mr Tosswell's overs are taken to its logical conclusion.
Step 4 - From the deduction in the above step we can work out the runs analysis of each of the batsmen.
Step 5 - We can then workout the fall of wickets, who got whom out and the last man standing with straight forward reasoning.
My answers are
Q 1: Mr Jenkins was dismissed by Speedwell and Mr Bodkins by Tosswell
Q 1: Mr Jenkins was dismissed by Speedwell and Mr Bodkins by Tosswell
Q 2: Mr Tomkins was not out
Q 3: Fall of wickets - 6/1, 12/2, 18/3, 23/4, 31/5, 41/6, 44/7, 58/8, 59/9, 60/10
