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I read a problem in the newspaper around 10 years back. Here is the problem

Team A scored 250 runs for 9 wickets in 50 overs. Team B was 250 for 0 in 49 overs. Eventually Team A won the match by virtue of losing fewer wickets. Hence Team B to lost 10 wickets in 1 over.

The main part of this question was no two players were dismissed in the same way. How is it possible to dismiss 10 players in an over such that all the dismissals are unique.

Partial Solution 9 players dismissed in an over

At the beginning of the over the following sequence of events takes place.

  1. Batsman 1 decides to get dismissed as Retired Out (different from Retired Hurt).
  2. Batsman 2 is Timed Out as he delays coming to the crease.
  3. The runner on the non-strikers end is dismissed via Run Out as he was backing up too much. Also called Mankading.

Effectively at this point we have dismissed three players without a single ball being bowled.

The next six balls allow for the following dismissals.

  1. Bowled
  2. Caught
  3. Leg Before Wicket
  4. Stumped
  5. Hit Wicket
  6. Handled the Ball

I am unable to find a way of dismissing the tenth batsman as we are now out of balls.

The only other option that I believe is Obstructing the field, though I am not sure if it is possible to be given out for obstructing the field before a ball is bowled.

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Has this situation ever happened in real time cricket? :D – Ganesh Babu Apr 21 '14 at 15:06

Some possibilities are there:

  1. If you are looking at not losing a match and making every batsmen out in unique ways without any extras, it is not possible:

  2. If the batting team requires more than 1 run:

    First three batsmen out, as you described, without facing a ball. The next batsman is Stumped out in wide ball so the wicket is fallen and still remain 6 balls to bowl and at least 1 run to win. Then next six batsmen is out as below:

    1. Bowled
    2. Caught
    3. Leg Before Wicket
    4. Hit the ball twice
    5. Hit Wicket
    6. Handled the Ball
  3. If you are looking at not losing a match when only 1 run is required to win and making every batsmen out in unique ways with extras are allowed:

    First three batsmen out, as you described, without facing a ball. While the next ball is going to be faced by the next batsman, the batsman attempting to steal a run during the bowlers run up. The umpire intervene and awards 5 runs penalty to fielding side for this unfair act. (here the ball is considered a dead ball - Law 42.16). Still the first delivery is to be bowled. The next batsman is Stumped out in wide ball so the wicket is fallen and still remain 6 balls to bowl and at least 1 run to win. Then next six batsmen is out as below:

    1. Bowled
    2. Caught
    3. Leg Before Wicket
    4. Hit the ball twice
    5. Hit Wicket
    6. Handled the Ball
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2  
correct answer. – Sports Fan Dec 10 '13 at 7:04

I have a complete solution, but the key part is that the title of this question has a wrong assumption.

Core Puzzle:

Team A scored 250 runs for 9 wickets in 50 overs. Team B was 250 for 0 in 49 overs. Eventually Team A won the match by virtue of losing fewer wickets. Hence Team B lost 10 wickets in 1 over. The main part of this question was no two players were dismissed in the same way. How is it possible to dismiss 10 players in an over such that all the dismissals are unique.

Title:

Dismiss 10 players in an over in unique ways without conceding a run

The title is not part of the original problem ; It is a wrong assumption that no runs have to be conceded.

Along the lines of your partial solution:
Wicket 1 is "Retired Out"
Wicket 2 is "Timed Out"
Wicket 3 is "Run Out (Mankading)"

Now the batsmen can do 3 things which give 5 penalty runs to fielding side :
Waste time (ball not even bowled), Damage the Pitch (ball not even bowled), Steal a run (may be one ball bowled)

Let us select the possibility of Wasting time.
After this happens, the fielding side score will be 255, the batting side will require 6 runs to win, with 6 balls remaining, with 7 wickets remaining. Bowler gives a 4 wide balls, which wicketkeeper blocks : 2 runs to win, 6 balls remaining, 7 wickets remaining.
Now bowler gives another wide ball and wicketkeeper fumbles, so batsmen try to take a run. When wicketkeeper tries to throw the ball to the bowler, the batsman obstructs his way, hence Wicket 4 is "Out obstructing the field".
Status : 1 run to win, 6 balls remaining, 6 wickets remaining.

Wicket 5 is "Bowled"
Wicket 6 is "Caught"
Wicket 7 is "Leg Before Wicket"
Wicket 8 is "Hit the ball twice"
Wicket 9 is "Hit Wicket"
Wicket 10 is "Handled the Ball"

Status : Team A 255 for 9 wickets, Team B 255 all out, Team A won the match by virtue of losing fewer wickets.

[[ Penalty Runs for fielding side : http://www.rulesofcricket.co.uk/the_rules_of_cricket/the_rules_of_cricket_law_42.htm ]]
[[ 10 Ways to get out : https://www.quora.com/How-can-you-get-out-in-cricket ]]

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Law 22.5(a) can provide the missing piece in your puzzle.

  1. Umpire miscounting

(a) If the umpire miscounts the number of valid balls, the over as counted by the umpire shall stand.

The last over becomes a 7-ball over due to the umpire miscounting.1 The 10th dismissal could be either (a) Hitting the Ball Twice or (b) Obstructing the Field.

The answer to your other sub-question on Obstructing the Field is that it is not possible before the ball is bowled, as covered in Law 37.1:

...
In particular, but not solely, it shall be regarded as obstruction and either batsman will be out Obstructing the field if while the ball is in play and after the striker has completed the act of playing the ball,
...


1 To make this more realistic, spread out the Retired Out, Timed Out, and Mankad Run Out between the other dismissals off legitimate deliveries instead of lumping them together before the start of the over, and add some drama.

For example, one batsman picks up a fight with the fielders, which leads to aggressive arguing and swearing for a prolonged duration. The batsman then storms off and is declared Retired Out.

A couple of balls later, someone is dismissed in a controversial manner, and the tension flares up again leading to more ugly scenes on the field. This spills over to the dressing room where members of the batting side (and maybe the reserve players and support staff of both teams) keep arguing loudly. Amidst the commotion, the next batsman forgets to step out and is declared Timed Out.

One or two balls later, with both sides brimming with rage, a Mankad Run Out happens! You can imagine what happens next. :-) In this scenario, it is easy to imagine the Umpire miscounting the over.

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Law 37 does not require an Obstructing the field dismissal to take place while the ball in in play - note the words "but not solely". (Even if it were required for the ball to be in play, under Law 23.5 the ball is in play as soon as the bowler starts his run up.) The first line of the Law is the most important one here: "Either batsman is out Obstructing the field if he wilfully attempts to obstruct or distract the fielding side by word or action." The second line merely highlights a possible application of the Law. – Spinner Apr 13 at 20:20

Based on the links provided on the following websites with regards to Obstructing the field, it is possible to be given out based on words, so technically you can be given out before the ball is bowled for Obstructing the field.

Here are some links

http://www.sportingpulse.com/get_file.cgi?id=955417

http://www.cricketforworld.com/2010/01/ways-of-batsman-dismissal-in-cricket.html

http://en.wikipedia.org/wiki/Obstructing_the_field

If it is possible to given out before the delivery is bowled, based on the words said by the guilty party, then we can indeed have 10 unique dismissals in an over without any extra balls being bowled.

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If I am not wrong the obstruction (either by a word or an action) only apply while the ball is in play. In other words he can not be given out when the ball is dead. – hims056 Dec 10 '13 at 9:49
    
Assume this scenario, the bowler is coming in to ball and the runner is standing outside the crease. Now the bowler warns the runner. When the bowler runs in again the runner is still outside, so the bowler decides to run him out (Mankading) but as he is in the process of doing it the runner throws his bat at the bowler to prevent him from doing it. Would it then be out as Obstructing the field, even though a ball has not been bowled. – Rahul Kadukar Dec 10 '13 at 9:52
    
Your scenario may be possible but still I am not sure if it is true as Law 37 says while the ball is in play and after the striker has completed the act of playing the ball. – hims056 Dec 10 '13 at 10:13
    
But here the runner prevented the baller from dismissing him. – Rahul Kadukar Dec 10 '13 at 10:16
    
The law applies for either batsman. (both) – hims056 Dec 10 '13 at 10:18

If the non-striker unsuccessfully attempts to stop the fielder taking the catch then he could be given out for obstructing the field on the same ball that the batsman is caught out.

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You cannot have both batsman out on the same ball and if a catch is prevented by the words or actions of the non striker the striker is out. see law 37.3 (lords.org/mcc/laws-of-cricket/laws/law-37-obstructing-the-field) – Ben Whyall Apr 12 at 15:12

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