Introduction to Booleans A Boolean is a two-state variable, which is generally assigned the values true or false. In a zebra puzzle, the use of Booleans allows us to identify boxes whose behavior follows the same rules: the boxes identified by the same Boolean are either all true or all false. Thanks to them, a […]
The complement technique is the simplest basic technique. Presence of a true sign When there is a true sign in a grid, we can complete the boxes in the corresponding row and column with false signs. By the very definition of the integram, there can only be one true sign per row and per column. […]
The square is one of the simple solving techniques that works within a grid. Finding them requires a keen eye! The principle Some false sign configurations can leave empty boxes on rows, boxes which must contain a true sign : Look at the yellow boxes forming a square: there must be at least one true […]
Repercussion is one of the most powerful and simplest techniques to implement when a zebra puzzle has multiple grids. It starts with a true sign on a central grid and projects an entire row into another grid. The row can contain false signs, true signs, and even Booleans. True sign on a central grid The […]
Merging is the inverse of repercussion. The technique can find pivot cells that are false, and, in some cases with Booleans, true cells . Two rows can produce a false pivot cell if combining the two rows results in a false row. NB: You must have a good understanding of the repercussion technique before tackling […]
Alternatives are the starting point for many techniques. This section does not cover any specific technique, but explains the principle of the alternative, which will be reused in specific techniques. In a statement, alternatives are mutually exclusive propositions. Simple case: in a grid Alice wears a blue, red or green swimsuit. The expression or corresponds […]
This technique is quite obvious. It works from an alternative. If a row contains an alternative, i.e., false signs and Booleans, with no empty cells, then rows containing an empty cell with the same number of false signs and the same Booleans, except one, can be completed with the missing Boolean.
This technique is used with two alternatives that differ by a single Boolean. Let x and y be two booleans . Let A be an alternative containing booleans (a,b,c…) and a boolean x . Let A’ be an alternative containing the booleans (a,b,c,…) identical to those of A, and the boolean y. In this case, […]
This very simple rule concerns Booleans. When a row contains n identical booleans, then they are false. Indeed, if they were true, there would be n true signs in the row, which is not possible by definition. In our videos, when Booleans don’t have names, it’s the color that makes them different. Here, they are […]
Let an alternative be formed of n Booleans. Any cell located at the intersection of the n Booleans of the alternative is false. The technique is simple when applied to a single grid, which is what motivated the creation of this rule. When applied to different grids, the technique is a reprise of the merging […]
When a Boolean is exposed to all terms of an alternative to which it does not belong, then it is necessarily false. This technique is a special case of invariance; it is much easier to implement. It is used only on Booleans, whereas invariance also concerns empty cells. The technique is also a generalization of […]
Implication is one of the advanced techniques. It works with Booleans and requires the establishment of hypotheses. It produces a simplification of the number of Booleans. It is an extremely powerful instruction and is widely used in puzzles marked “often difficult.” The implication is not easy to understand. To help, we can translate it with […]
Invariance is one of the advanced techniques. It requires the establishment of hypotheses. We choose empty cells (or cells containing Booleans) and successively set them to true and false, then observe the result. Let A and B be two empty boxes or boxes containing booleans. If, whatever the true or false state of A, B […]
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