A 1930 Cricket Puzzle by Sir Artur Eddington

[harsh.ag]

Sir Donald Bradman once wrote about a puzzle given to him by a famous astrophysicist, Sir Arthur Eddington, in 1930. He went on to explain that he had taken two decades to solve the puzzle and finally cracked it while on a ship to England to play against the British in 1948. He also said he would be happy to have someone else give it a try.


Here's Don Bradman's 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?

Time to let CWers have a crack at it If you know the answer, or manage to solve the puzzle, please PM me instead of posting the answer on this thread.

 

[harsh.ag]

This is one tough nut. It took Bradman around two decades. So, where are all the stats aficionados? Go linear on this ****

 

[harsh.ag]

I have been on this for almost three hours now, and am finding it incredibly difficult to crack.

 

[harsh.ag]

I think I have figured this out (at least one way of doing so..). I am posting the first part of my solution:

1st over - Bowled by Pitchwell. Atkins on strike. Single. Bodkins on strike.


2nd over - Bowled by Speedwell. Atkins on strike. Four.


3rd over - Bowled by Pitchwell. Bodkins on strike. Maiden.


4th over - Bowled by Speedwell. Atkins on strike. Single.


5th over - Bowled by Pitchwell. Atkins on strike. Out. 6/1 (Atkins b.Pitchwell for 6). Dawkins on strike. Single. Bodkins on strike.


6th over - Bowled by Speedwell. Dawkins on strike. Four.


7th over - Bowled by Pitchwell. Bodkins on strike. Maiden.


8th over - Bowled by Speedwell. Dawkins on strike. Single. Bodkins on strike.


9th over - Bowled by Pitchwell. Dawkins on strike. Out. 12/2 (Dawkins b.Pitchwell for 6). Hawkins on strike. Four. Single. Bodkins on strike.

10th over - Bowled by Speedwell. Hawkins on strike............

 

[DavidL]

I received Sir Don's book 'The Art of Cricket' as a birthday gift during the late 1980s. I managed to solve Sir Arthur's scoring problem, which appears on page 224. During the 2000s I discovered two other solutions published on the net, and I exchanged messages with one of these people, who was kind enough to include my solution on his webpage alongside his own. Unfortunately attempting to reach this page nowadays causes a 404 'Not found' error.

[EDIT] I was forced to delete links to the second person's analysis as it was causing an error: "Oops! We ran into some problems.
Your content can not be submitted. This is likely because your content is spam-like or contains inappropriate elements. Please change your content or try again later. If you still have problems, please contact an administrator."

As a possible clue, there are multiple correct scoring combos, although all yield the same answers to the 3 questions asked. Possible solutions involve interchanging the scoring shots of Atkins, Dawkins and Hawkins (who scored 6 runs each). However, because Bodkins must remain scoreless during this period, this does not alter the score at the fall of each of the first 3 wickets.

Some more clues, as quoted by Sir Don:
"To illustrate the way one has to work, just let me say this. Tosswell, who bowls seven overs, of which five are maidens, for 31 runs, must have had seven fours and three singles hit off him because we are told the total score was made up of fours and singles. No other combination of 12 balls can possibly give you a total of 31 runs. That is the kind of hypothesis which must be applied throughout."

 

[Coronis]

Maybe Bradman doesn’t get out for a duck in his final innings if he wasn’t so focused on the puzzle.