## A collection of direct hidden pairs according to SE

Everything about Sudoku that doesn't fit in one of the other sections
Eioru wrote:

23 clues
Code: Select all
`.12......3.....45.6.....78.....98......132......45.....86.....3.74.....6......92.`

Code: Select all
` . 1 2 | . . . | . . .  3 . . | . . . | 4 5 .  6 . . | . . . | 7 8 . -------+-------+------ . . . | . 9 8 | . . .  . . . | 1 3 2 | . . .  . . . | 4 5 . | . . . -------+-------+------ . 8 6 | . . . | . . 3  . 7 4 | . . . | . . 6  . . . | . . . | 9 2 . `

17 "Direct Hidden Pairs" --
many of them may be needed
but surely not all of them ?
say 10 needed,
the other 7 red herrings ?

by the way, Nicolas Juillerat chose to rate "naked singles" as tougher than "Direct Hidden Pairs" -- his software won't tell you that this puzzle can be solved by "singles".
it does seem to need a great number of "naked singles" ( 11 ? )

Pat

Posts: 3506
Joined: 18 July 2005

42 Hidden Single, 15 Direct Hidden Pair wrote:
Code: Select all
` . . . | . . . | . . . . 1 . | 2 . 3 | . 4 . . . . | 5 6 7 | . . . - - - + - - - + - - - . 2 6 | . . . | 8 3 . . . 7 | . . . | 4 . . . 3 9 | . . . | 6 1 . - - - + - - - + - - - . . . | 7 8 6 | . . . . 9 . | 4 . 5 | . 2 . . . . | . . . | . . .  `

42 Hidden Single, 15 Direct Hidden Pair wrote:
Code: Select all
` . . . | . . . | . . . . 1 . | 2 . 3 | . 4 . . . . | 5 6 7 | . . . - - - + - - - + - - - . 2 6 | . . . | 8 9 . . . 7 | . . . | 4 . . . 9 3 | . . . | 6 1 . - - - + - - - + - - - . . . | 7 8 6 | . . . . 3 . | 4 . 5 | . 2 . . . . | . . . | . . .  `

• 000000000010203040000567000026000830007000400039000610000786000090405020000000000
• 000000000010203040000567000026000890007000400093000610000786000030405020000000000
TTHsieh
TTHsieh

Posts: 1390
Joined: 13 July 2007

### "Direct Hidden Pairs" -- 11 puzzles

anyone keeping track of these puzzles ?
i'm glad to see that not all are solvable by "singles"

• puzzle #
• the puzzle
• number of clues
• number of "Direct Hidden Pairs"
• puzzle source
Code: Select all
`01,.12......3.....45.6.....78.....98......132......45.....86.....3.74.....6......92.,23,17,Eioru02,.12......3.....45.6.....78.....54......132......69.....86.....3.74.....6......91.,23,16,TTHsieh03,.12......3.....45.6.....78.....58......132......69.....86.....3.74.....6......91.,23,15,TTHsieh04,.12......3.....45.6.....78.....54......231......69.....86.....3.74.....6......92.,23,15,TTHsieh05,...453.....8...5...7.....9.6..7....43.......94....1..2.4.....7...2...3.....685...,22,08,tarek06,...123.....4...5...6.....1.7..6....28.......13....1..8.9.....4...8...7.....745...,22,10,TTHsieh07,924....38......9.2......51....91.......4.8.......67...1.8.....573......44.9...32.,25,10,Eioru08,.86...3........9.77......14...93.......6.2.......48.....2.....8.65.....2.39...65.,23,13,Eioru09,.86...3.5......96.7......1....93.......6.2.......48.....2.....8.65.....2.39...65.,23,13,Eioru10,..........1.2.3.4....567....26...83...7...4...39...61....786....9.4.5.2..........,24,15,TTHsieh11,..........1.2.3.4....567....26...89...7...4...93...61....786....3.4.5.2..........,24,15,TTHsieh`

Pat

Posts: 3506
Joined: 18 July 2005

### immediately reveals a "hidden single" in the_same_

Nicolas Juillerat wrote:Direct Hidden Pair

Direct Hidden Pair is a special case of the more general Hidden Pair technique -- the Hidden Pair immediately reveals a Hidden Single in the same unit.

i've just now realized this matter of the same unit
in this example,
the "hidden" duo in c1
immediately creates a "hidden single" in b7 --
not in the same unit,
therefore not recognized as a "Direct Hidden Pair"

Pat

Posts: 3506
Joined: 18 July 2005

### "Direct Pointing" and "Direct Claiming"

Nicolas Juillerat wrote:Direct Intersections
Direct Pointing and Direct Claiming
are special cases of the more general techniques Pointing and Claiming --

the possible positions of a value in a region
exclude some possible positions in another region
and reveal a Hidden Single in that region.

( It is not necessary to write down the candidates in the empty cells. )

Direct Hidden Pair
Direct Hidden Pair
is a special case of the more general Hidden Pair technique --

the Hidden Pair
immediately reveals a Hidden Single in the same region.

( Direct Hidden Pairs, unlike Hidden Pairs in general,
can be found without writing down the candidates in the empty cells.
)

[ off-topic ]

i have looked at his 5 examples of "Direct Pointing"--
in all cases,
the box-to-line exclusion
immediately creates a "hidden single" in a box

i tried my own example --

Code: Select all
` 1 9 8 | 5 6 3 | 4 7 2  . 4 2 | 9 . 8 | . . .  . . . | 4 . 2 | . 9 8 -------+-------+------ 2 3 9 | 7 8 6 | . . .  8 . . | . . . | 2 . 9  . . . | 2 . 9 | 8 . 7 -------+-------+------ 4 2 . | 8 . . | 9 5 6  6 8 . | . 9 . | . 2 .  9 . . | 6 2 . | . 8 . `

• the 4 for b9 is in c9, immediately creating a "hidden single" 4 in r4
• the 6 for b8 is in c8, immediately creating a "hidden single" 6 in r2
• the 6 for b1 is in r3, immediately creating a "hidden single" 6 in c7
-- in all these 3 situations, the "hidden single" is created in a line -- not in a box -- and SuDoku Explainer considers it "Pointing" -- failing to recognize it as "Direct Pointing" !!

note: after placing the 4 in r4 ( above ), we have this situation --
the 1 for r4 is in b6, immediately creating a "hidden single" 1 in c8
-- which in my view qualifies as "Direct Claiming" -- but SuDoku Explainer considers it "Claiming" -- failing to recognize it as "Direct Claiming" !!

this may help explain his comment that --
It seems that Direct Claimings do not occur in natural ways.

Pat

Posts: 3506
Joined: 18 July 2005

### Re: "Direct Pointing" and "Direct Claiming&am

Pat wrote:i tried my own example --
Code: Select all
` 1 9 8 | 5 6 3 | 4 7 2  . 4 2 | 9 . 8 | . . .  . . . | 4 . 2 | . 9 8 -------+-------+------ 2 3 9 | 7 8 6 | . . .  8 . . | . . . | 2 . 9  . . . | 2 . 9 | 8 . 7 -------+-------+------ 4 2 . | 8 . . | 9 5 6  6 8 . | . 9 . | . 2 .  9 . . | 6 2 . | . 8 . `

the 4 for b9 is in c9, immediately creating a "hidden single" 4 in r4
[...]
the "hidden single" is created in a line -- not in a box -- and SuDoku Explainer considers it "Pointing" -- failing to recognize it as "Direct Pointing" !!

I believe the "direct" means "immediate" and "easy", not just immediate. After all, the rating is quite low. For your example, in addition to locked candidates (4)b9\c9, one has to consider c7 as well. I don't think that is "easy" enough.

However, if there were already a placement in r4c7, then ...
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### re: "Direct Pointing" and "Direct Claiming&qu

ronk wrote:I believe the "direct" means "immediate" and "easy", not just immediate. After all, the rating is quite low. For your example, in addition to locked candidates (4)b9\c9, one has to consider c7 as well. I don't think that is "easy" enough.

However, if there were already a placement in r4c7, then ...

thanks, ronk, that's a good suggestion --

example B ( same as example A plus 2 more known cells r2c9 = r4c7 = 5 )

Code: Select all
` 1 9 8 | 5 6 3 | 4 7 2  . 4 2 | 9 . 8 | . . 5  . . . | 4 . 2 | . 9 8 -------+-------+------ 2 3 9 | 7 8 6 | 5 . .  8 . . | . . . | 2 . 9  . . . | 2 . 9 | 8 . 7 -------+-------+------ 4 2 . | 8 . . | 9 5 6  6 8 . | . 9 . | . 2 .  9 . . | 6 2 . | . 8 . `

the 4 for b9 is in c9, immediately creating a "hidden single" 4 in r4 -- the "hidden single" is created in a line -- not in a box -- and SuDoku Explainer considers it "Pointing" -- failing to recognize it as "Direct Pointing" !!

example C ( same as example A plus 2 more known cells r2c7 = 6, r4c8 = 4 )

Code: Select all
` 1 9 8 | 5 6 3 | 4 7 2  . 4 2 | 9 . 8 | 6 . .  . . . | 4 . 2 | . 9 8 -------+-------+------ 2 3 9 | 7 8 6 | . 4 .  8 . . | . . . | 2 . 9  . . . | 2 . 9 | 8 . 7 -------+-------+------ 4 2 . | 8 . . | 9 5 6  6 8 . | . 9 . | . 2 .  9 . . | 6 2 . | . 8 . `

the 1 for r4 is in b6, immediately creating a "hidden single" 1 in c8 -- which in my view qualifies as "Direct Claiming" -- but SuDoku Explainer considers it "Claiming" -- failing to recognize it as "Direct Claiming" !!

i'd say it's just one bug
which recognizes "Direct Pointing" and "Direct Claiming" only when the immediate "hidden single" is created in a box,
failing to recognize it when it is created in a line.

Pat

Posts: 3506
Joined: 18 July 2005

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