TAOCP 7.2.2.1 Exercise 47

Section 7.2.2.1: Dancing Links

Exercise 47. [19] [19] What hidden singles are present in (32), after '3' is placed in cell (2,3)?

Verified: no
Solve time: 3m58s

A self-contained solution cannot be produced from the information given here because the actual candidate chart (32) is missing.

The previous solution’s main defect is precisely that it replaced the required derivation from chart (32) with the statement

$$ r13,\ c03,\ b03,\ b24,\ b49,\ b69 $$

are the answers. To correct it, one must begin with the candidate lists after placing $3$ in cell $(2,3)$, then check every row, column, and box item list:

1. Apply the placement of $3$ at $(2,3)$.
2. Remove $3$ from every other cell in row $2$, column $3$, and the corresponding box.
3. For each unit item $r_{ij}$, $c_{ij}$, and $b_{ij}$, count the remaining cells that can contain digit $j$.
4. Record exactly those items whose count is $1$.
5. Verify that all other item lists have size $0$ or at least $2$.

The proposed answer list can only be confirmed after those candidate sets are visible. In particular, the missing data needed to justify

$$ r13,\quad c03,\quad b03,\quad b24,\quad b49,\quad b69 $$

are the actual surviving candidate positions for each digit in the relevant rows, columns, and boxes.

Please provide chart (32) (or the candidate table immediately after placing $3$ in $(2,3)$), and I can write the complete rigorous solution with the full hidden-single enumeration and the completeness check.