Arthur Eddington’s Cricket problem

The following is a problem set by Sir Arthur Eddington (which appeared in Caliban’s column in The New Statesman).

Extract from the score of a cricket match between Eastershire and Westershire:

Eastershire — Second Innings
A.A.Atkins	6
Bodkins	8
D.D.Dawkins	6
Hawkins	6
Jenkins(J.)	5
Larkins	4
Meakins	7
Hon. P.P.Perkins	11
Capt. S.S.Simkins	6
Tomkins	0
Wilkins	1
Extras	0
Total	60

Bowling Analysis
	Overs	Mdns.	Runs	Wkts.
Pitchwell	12.1	2	14	8
Speedwell	6	0	15	1
Tosswell	7	5	31	1

      The score was composed entirely of singles and fours. There were no catches, no-balls or short runs.
      Speedwell and Tosswell each had only one spell of bowling. Pitchwell bowled the first over, Mr Atkins taking the first ball. Speedwell was the other opening bowler.
      Whose wickets were taken by Speedwell and Tosswell?
      Who was not out?
      What was the score at the fall of each wicket?

Tosswell conceded 31 runs in 12 balls (only 2 overs were not maidens)
There must be at least 3 singles.
So he conceded 28 runs in 9 balls.
If 4 of these were singles, that would leave 24 runs conceded in 5 balls.
We conclude that Tosswell concedes 7 fours and 3 singles

Pitchwell concedes in 10 of his 12.1 overs, so he must concede at most 1 four and at least 10 singles,

Speedwell concedes in all of his 6 overs, so we can make no constraint on how his 15 runs are conceded.

There are 25.1 overs made up of:

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
P	S	P	S	P	S	P	S	P	S	P	S	T	P	T	P	T	P	T	P	T	P	T	P	T	P

The maximum number of fours that can be scored by eash batsman is:

Eastershire — Second Innings		max 4s
A.A.Atkins	6	1
Bodkins	8	2
D.D.Dawkins	6	1
Hawkins	6	1
Jenkins(J.)	5	1
Larkins	4	1
Meakins	7	1
Hon. P.P.Perkins	11	2
Capt. S.S.Simkins	6	1
Tomkins	0	0
Wilkins	1	0
Extras	0
Total	60	11

There are no more that 4 fours in the first 12 overs, before Tosswell comes on in the 13th over.
Also at least one wicket has fallen, and at least 15 runs have been scored.
As Pitchwell concedes at most 1 four, there can be no more that 8 fours after the change of bowlers, and at least 7.
So there can be no more than 4 fours in the first 12 overs, and at least 1 wicket.

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
P	S	P	S	P	S	P	S	P	S	P	S	T	P	T	P	T	P	T	P	T	P	T	P	T	P

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
P	S	P	S	P	S	P	S	P	S	P	S	T	P	T	P	T	P	T	P	T	P	T	P	T	P

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
P	S	P	S	P	S	P	S	P	S	P	S	T	P	T	P	T	P	T	P	T	P	T	P	T	P