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EXAMPLES.DOC
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1996-02-20
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PC-Sherlock - Examples of logical analysis:
-------------------------------------------
It's very interesting to know that there's no simple formula for
winning in this logical game. Although, I am showing you a few
example games to show how I arrived at my guesses, please don't try
to look for a definite pattern in my play. The games generated are
random and each game requires original thinking.
You must have already seen the topic "Examples of deduction" in the
online tutorial. If not, please read the online tutorial before
looking at these examples. Here, I'm showing examples of 3, 4 and 5
digit games. Note that 3 and 5 digit games are available only in the
registered version. It's my opinion that the 3 digit game is the
easiest to play.
EXAMPLE 1: (3 digit game)
=========================
CHANCE 1: Asked 123, got 0 bull, 1 cows
CHANCE 2: Asked 456, got 1 bulls, 1 cows
Initial assumption:
Assume that '4' is the bull, '6' and '2' are cows.
CHANCE 3: Asked 462, got 0 bulls, 2 cows
Deduction starts:
Chances of '4' and '6' being present are greater than '2' being
present. So we change the position of '4' and '6' and ask another
digit from chance 1.
CHANCE 4: Asked 346, got 3 bulls
WE WIN THE GAME! Of course, here it was lucky to get two of our
assumptions right. Otherwise, it would have taken more chances.
EXAMPLE 2: (3 digit game)
=========================
CHANCE 1: Asked 123, got 2 bulls, 0 cows
CHANCE 2: Asked 456, got 0 bulls, 1 cows
Initial assumption:
Assume that '1' and '2' are the bulls and '4' is the cow.
CHANCE 3: Asked 124, got 1 bull , 0 cows
Deduction starts:
Assume '1' to be the bull. Then '2' and '4' are absent. Hence, '3' is
present and is a bull in chance '1'. So our number is 1X3 where X is
either '5' or '6' from chance 2. Now, X can't be '5' as the clue for
chance 2 is 1 cow. Hence, X is '6'. So the number to ask is 163.
CHANCE 4: Asked 163, got 3 bulls
WE WIN THE GAME! Note that unlike the previous example, this win can't
be attributed to just luck. The deduction worked!
EXAMPLE 3: (4 digit game)
=========================
CHANCE 1: Asked 1234, got 1 bulls, 1 cows
CHANCE 2: Asked 5678, got 0 bulls, 2 cows
Initial Assumption:
Assume '3' to be the bull and '2', '5' and '6' to be the cows. We ask
a guess where the cows change position whereas bull does not.
CHANCE 3: Asked 6532, got 3 bulls, 0 cows
Deduction starts:
We got lucky here to get 3 bulls. Now we assume that we got '5' and
'6' right as bulls. But we are not sure whether '3' was the bull or
the '2' became a bull on a changed position. Let's assume that '2'
became the bull. That means '3' is absent and the number is 65X2
where X can be '1' or '4'. Let's assume X to be '4'. So we ask 6542.
CHANCE 4: Asked 6542, got 2 bulls, 0 cows.
Deduction continues:
Our clues got reduced in number from 3 bulls to 2 bulls! So most
probably, our basic assumption that '5' and '6' are bulls seems to be
wrong. Only one of '5' and '6' is a bull. In that case, looking at
chance 3, digits '3' and '2' are definitely the bulls. If we assume
'6' to be the third bull, the number is 6X32. Now from chance 2, X
can be '7' or '8'. Let's assume X to be '7'. So the number to ask
is 6732.
CHANCE 4: Asked 6732, got 4 bulls
WE WIN THE GAME!
EXAMPLE 4: (5 digit game)
=========================
CHANCE 1: Asked 12345, got 0 bulls, 1 cows
Elimintation technique:
It means only one of above 5 digits is present. Let's repeat three of
the above digits for quicker elimination of digits.
CHANCE 2: Asked 67123, got 1 bulls, 0 cows
Deduction starts:
Since total seven digits asked in first two guesses covered only 1
clue, we deduce that remaining three digits '8','9' and '0' are
definitely present. Also, it is more probable that the bull is from
'1', '2' and `3' instead of from '6' and '7' as '1', '2' and '3' have
repeated in two chances and have changed positions. We aren't sure
which one so let's repeat '1' and '2' and ask the remaining three
digits in other positions.
CHANCE 3: Asked 80129, got 0 bulls, 3 cows
Deduction continues:
Since digits '8', '9' and '0' are definitely present as per the
previous deduction, we conclude that '1' and '2' are absent. So, from
chance 2, digit '6', '7' or '3' was the bull. Assume '6' to be the
bull. In that case '1', '2' and '3' are absent and we select the next
digit from chance 1 to be the cow which is digit '4'. Let's change
positions of '8', '9' and '0' (all cows) and ask 69804.
CHANCE 4: Asked 69804, got 3 bulls, 1 cows
Deduction continues:
This means choice of '4' was wrong in the last step. Hence, we select
the next digit '5' from chance 1. From chance 4, let's assume '6',
'9' and '8' to be the bulls. Hence, we ask 69850. Note that we can't
ask '5' in the last position as it was a cow there in chance 1.
CHANCE 5: Asked 69850, got 2 bulls, 3 cows
Deduction continues:
Good! We at least got all the 5 digits now. Let's shift the positions
of three assumed cows and ask again.
CHANCE 6: 69508, got 5 bulls
WE WIN THE GAME!
END OF EXAMPLES
==================================================================
If you haven't registered, please register PC-Sherlock and support
independent development. Please see the ordering instructions in the
accompanying file ORDER.DOC.
Sanjay Kanade
(Author of PC-Sherlock)
email: 71303.20@compuserve.com