Puzzle that requires use of one naked pair

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Puzzle that requires use of one naked pair

Postby Pi » Wed Nov 16, 2005 10:55 pm

Does anyone have a puzzle that i can use to test my program, i need one that requires use of one naked pair.

-pi
Pi
 
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Postby r.e.s. » Thu Nov 17, 2005 2:35 am

I'm not sure, but isn't it tricky to say that a naked pair is required?
E.g., here's one that can be solved using just one naked pair ...
Code: Select all
+-------+-------+-------+
| 1 . . | 7 3 . | . 8 . |
| . . 6 | 9 . 8 | 7 . . |
| . . 7 | 6 . . | . 3 . |
+-------+-------+-------+
| . . 3 | . . . | . . 5 |
| . 4 . | . 2 . | . 9 . |
| 7 . . | . . . | 4 . . |
+-------+-------+-------+
| . 3 . | . . 1 | 5 . . |
| . . 1 | 2 . 9 | 3 . . |
| . 9 . | . 7 3 | . . 2 |
+-------+-------+-------+
...but it can also be solved without using any naked pairs.
r.e.s.
 
Posts: 337
Joined: 31 August 2005

Postby Pi » Thu Nov 17, 2005 5:17 pm

Thanks but i really need one than requires the naked pair
Pi
 
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Joined: 27 May 2005

Postby tso » Thu Nov 17, 2005 6:00 pm

I'll go out on a short limb and say that it's impossible for a puzzle to require using a naked pair to make eliminations. There will always be other ways, though they may be subjectively more complex or difficult to find, to bypass the point -- either by finding the same elimination or following a completely different route to the solution. Most obviously, if there is a naked subset, there will be some sort of hidden subset in the same house.

Also, naked pairs can be thought of a degenerate versions of other higher level tactics, for example, forcing chains...

Given three cells -- a, b and c -- in a row:
[12][12][123]

If a=1, then b=2, then c<>2
If a=2, then c<>2
therefore, c<>2

If a=2, then b=1, then c<>1
If a=1, then c<>1
therefore, c<>1

Since c<>1 or 2, then c=3


If and only if you insist on applying tactics in a set (and ultimately arbitrary) order can you ask "Is there a puzzle that requires a naked pair and no higher level deductions to solve?"
tso
 
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Postby Pi » Thu Nov 17, 2005 6:44 pm

I don't mind if the puzzle can be solved using harder tactics but i need one which at some point has no hidden singles o naked singles but does have a naked pair, i don't care if there is also a chain or hidden triplet or something
Pi
 
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Postby r.e.s. » Thu Nov 17, 2005 7:04 pm

tso wrote:There will always be other ways, though they may be subjectively more complex or difficult to find
The subjective aspect is important, istm; e.g., in the puzzle I posted, one alternative to using naked pairs is to reason that because a certain column contains a certain candidate only in two cells of its intersection with a certain box, that candidate can be eliminated elsewhere in that box -- a deduction arguably as "simple" as one based on a naked pair.
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Joined: 31 August 2005

re: puzzle requiring a duo

Postby Pat » Tue Nov 22, 2005 5:26 pm

Pi wrote:Does anyone have a puzzle that i can use to test my program,
i need one that requires use of one naked pair.

i really need one than requires the naked pair

I don't mind if the puzzle can be solved using harder tactics
but i need one which at some point has no hidden singles or naked singles but does have a naked pair,
i don't care if there is also a hidden triplet or something


Code: Select all
 1 . . | 4 . 7 | . . 3
 . 7 . | . . . | . 1 .
 . . 2 | . . . | 5 . .
-------+-------+------
 . . 1 | 7 . 4 | 2 . .
 . . 8 | 3 . 2 | 6 . .
 . . 7 | 5 . 8 | 1 . .
-------+-------+------
 . . 4 | . . . | 7 . .
 . 5 . | . . . | . 8 .
 2 . . | 8 . 6 | . . 4


enjoy!

- Pat
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