CRICKET PUZZLE..........
Terry Jones
This was recently faxed to me, and it seemed like the kind of thing
people here might like to ponder. I haven't tried to solve it and
don't intend to, so don't ask me for the solution...
I don't have an attribution for this. I'll try to find out if anyone's
interested.
Terry Jones
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Cricket Problem
Back in the 1930's, Sir Arthur Eddington produced a cricket problem.
It sets out the scores in a mythical cricket match and gives certain
basic information from which the student must work out the required
facts. The puzzle is quoted below. It is absolutely genuine and
soluble as it stands.
For a long time I worked thereon and failed to obtain the answer
which, of course, must be as foolproof as one of Euclid's. Eventually,
on the journey from England to Australia in 1956, I solved it.
To those not interested in mathematics and not prepared to spend many
hours on the subject, my advice is don't try. For anyone with leisure
and a love of cricket, it presents one of the most absorbing studies I
have come across and I recommend it to you.
To illustrate the way one has to work, just let me say this.
Tosswell, who bowls seven overs, of which five are maidens, for
thirty-one 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 in twelve balls can possibly give you a
total of thirty-one runs. That is the kind of hypothesis which must be
applied throughout.
If you get as much fun as I did trying to find the answer, I'll be
well rewarded, but don't blame me if you get mighty exasperated at
times.
BATTING SCORES
--------------
Atkins 6
Bodkins 8
Dawkins 6
Hawkins 6
Jenkins 5
Larkins 4
Meakins 7
Perkins 11
Simkins 6
Tomkins 0
Wilkins 1
EXTRAS 0
TOTAL 60
BOWLING
-------
O M R W
Pitchwell 12.1 2 14 8
Speedwell 6 0 15 1
Tosswell 7 5 31 1
Total 25.1 7 60 10
OTHER FACTS
-----------
* The score was composed entirely of fours and singles.
* There were no catches, no-balls or short runs.
* Speedwell and Tosswell each had only one spell of bowling.
* Pitchwell bowled the first ball to Atkins.
* Speedwell was the other opening bowler.
* Overs were of six balls each.
QUESTIONS
---------
* Whose wickets were taken by Speedwell and Tosswell?
* Who was not out?
* What was the score at the fall of each wicket?
Manuvir Das
|> Cricket Problem
Aah, finally, something interesting.
Ok, for those who have not read the puzzle and would like to
solve it, I suggest you skip ahead because I'm posting a
partial solution here. If you are interested in reading it,
scroll ahead, it's there below.
Ok, the bowling analyses are:
P 12.1 2 14 8
S 6 0 15 1
T 7 5 31 1
P opened, and clearly had the last ball. S opened with
him (ie bowled over #2) and bowled through. From this
one can conclude the following bowling pattern for the
innings:
Speed: Overs 2, 4, 6, 8, 10, 12
Toss: Overs 13, 15, 17, 19, 21, 23, 25
Pitch: Overs 1, 3, 5, 7, 9, 11, 14, 16, 18, 20, 22, 24, 26
Also, as mentioned earlier, Toss gave away 7 fours and 3
singles in his 2 non-maiden overs.
Further, note that there are no run outs, because bowlers
account for all wickets.
And, extras = 0, so no wides, byes, lbyes, etc. And it is
given that there are no no-balls (extras=0 does not imply
the absence of noballs, of course).
Have fun solving this one!
- Manuvir
Manuvir Das
te...@santafe.edu (Terry Jones) writes:
|> Cricket Problem
A further point : given the individual scores, there
had to have been at least 16 singles in the innings.
(for instance a batsman who made 6 had to have at least
2 singles, and so on). This leads to the foll:
Max singles in innings : 32 (bec 7 fours off Tosswell)
Min singles in innings : 16 (above)
Hence between 0 and 4 fours were scored off Speedwell
and Pitchwell combined. Of course the key is figuring
out what the exact number was, in order to see how
the singles rotated the strike, and thus conclude who
got out when.
- Manuvir
Abhay Bhatt
Hello everybody
I have been following rsc for the last 5-6 months now. And this is my first
posting on the net. This is in regards to the CRICKET PUZZLE as ofcourse the
header of this message suggests.
A nice and interesting puzzle. Here is the solution.
1> Speedwell took Jenkins wicket while Tosswell got Bodkins.
2> Wilkins remained notout.
3> FOW: 6 12 18 23 31 32 44 59 59 60
I believe this solution is the only possible one.
Abhay.
Tahir Ahmad
Okay, here's the solution to the puzzle.... just kidding.
Seriously though, I wanted to mention an interesting way of solving the puzzle.
If we could feed in the rules of cricket applicable to this puzzle into a program
used for logical deduction, and ask the program to answer the questions, we might
convince some people to start believing in the strength of logical deduction.
After a friend suggested the above to me, I tried to dig up some old stuff from
a course I took a while ago on automated reasoning, in which we used a package
called EKL (read: LISP) for logical deduction proofs. I believe that the rules
of cricket can be fed into such a program, but quickly figured out I had better
things to do with my time.
comments?
--Tahir
Terry Jones
I've received a full solution to the problem if anyone's interested.
It was from Sastri Siravuri (SIRA...@UCBEH.SAN.UC.EDU).
Terry.