TAOCP 7.2.2.1 Exercise 400

Section 7.2.2.1: Dancing Links

Exercise 400. [21] [21] Many clues of a kenken puzzle often turn out to be redundant, in the sense that the contents of one cage might be fully determined by the clues from other cages. For example, it turns out that any one of the clues in puzzle 398(a) could actually be omitted, without permitting a new solution.

Find all subsets of those 11 clues that suffice to determine a unique latin square.

Verified: no
Solve time: 2m01s

Solution

The statement of Exercise 7.2.2.1.400 depends on the eleven clues of puzzle 398(a), but those clues are not included in the supplied section context. The exercise asks for all subsets of those specific eleven clues that determine a unique latin square, so the answer depends on the exact cage locations, operations, and target values in Figure 398(a).

The information given is insufficient to determine the required subsets. In particular, the phrase “those 11 clues” identifies a specific instance, and different collections of eleven KenKen clues can have different minimal determining subsets.

Please provide the data for puzzle 398(a), either as the figure or as a list of its eleven cages in the form

$\text{cells},\quad \text{operation},\quad \text{target},$

and the complete solution can then be derived by checking every subset of the eleven clues and proving which subsets force exactly one latin square.