The New Sudoku Players' Forum

[BigJ16]

. . 4 | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. 4 . | . . . | . . .
. . . | . . . | . . .
------+-------+------
5 . . | . . . | . . .
x . . | . . . | . . .
. . . | . . 4 | . . .


At the position x according to a technique the only solution is 4.
Unique Candidate

You know that each block, row and column on a Sudoku board must contain every number between 1 and 9. Therefore, if a number, say 4, can only be put in a single cell within a block/column/row, then that number is guaranteed to fit there. This example illustrates the number 4 as the unique candidate for the cell marked.

I don't understand why that is the case.

[Pat]

the 4 for that box
has only one possible cell (marked x)

we usually call this: "hidden single"

Code: Select all


. . 4 | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. . . | . . . | . . .
. 4 . | . . . | . . .
. . . | . . . | . . .
------+-------+------
5 . . | . . . | . . .
x . . | . . . | . . .
. . . | . . 4 | . . .



[JasonLion]

There must be a 4 somewhere in block 7. It can't be in column 3 due to the 4 in block 1, it can't be in column 2 due to the 4 i block 4, so it must be in column 1. It can't be in row 7 because there is alreday a 5 there. it can't be in row 9 because of the 4 in block 8, so the only remaining place it can possibly be is R8C1. If you filled out an possibly valid pencil marks the only pencil mark for 4 would be in that same cell, which is part of why the solving technique is called hidden single.

[rjamil]

Hi BigJ16,

In addition to above-mentioned JasonLion explanation, there might be a chance for other numbers except 5 to put at the position x. But, if anything other than number 4 is placed at position x then there will be no position left in box 7 for number 4.

Think about box 7 for number 4 and position x.

R. Jamil

[SpAce]

It's actually a doubly hidden single, as there's only one cell available for 4 in both box 7 and column 1; thus it's "hidden" in two houses. If there were a 4 in r7c789, it'd be triply hidden (only one place available in row 8 as well). Box-based hidden singles (and subsets) are easier to find than line-based ones, but since this is both, it's doubly easy (a bit ironically). In general, hidden singles and subsets are easier to find by looking at the givens and solved cells than pencil marks. On the other hand, naked singles and subsets are harder to find without pencil marks.