The alternatives

The alternatives are coded in the following grid:

An alternative

What is an alternative? It’s a proposition with several terms, only one of which is true. In Actilud, generated statements can propose two-term alternatives:

Alice is second or fourth.
Either Bob is wearing a blue jersey or he is drinking apple juice.

In a two-term alternative, one of the two terms is true and the other is false. It is not possible for both to be true or both to be false. The mathematical symbol for an alternative is the exclusive or (⊻).

More generally, an alternative can have multiple terms. Also, in our editor, the alternatives window allows you to code up to 6 terms for a 5×5 puzzle ( n+1 terms for an n x n puzzle). In an n -term alternative , only one term is -necessarily- true and all the others are -necessarily- false. They cannot all be false. Only one term must be true.

Coding alternatives

It all depends on the alternative.

When the alternative occurs in only one grid , false signs are sufficient:

Alice is second or fourth.

If Alice is second or fourth, she cannot be first, third, or fifth. So the coding is very simple.

When the alternative occurs on several grids, then you must use booleans and the grid of alternatives:

Either Bob wears a blue jersey or he drinks apple juice.

When the alternative covers several grids, we use different booleans for each term of the alternative; but, to indicate to the solver that it is an alternative, we place the same booleans in a row of the alternatives grid – regardless of their position in the row.

By the way, if you use the solver in the above situation, it suggests putting a false sign at the intersection of blue (“bleu”) jersey and apple (“pomme”): in fact, the wearer of the blue jersey cannot drink apple juice.

Behavior of Booleans in the Alternatives Grid

Be careful, the behavior is logical but can be surprising.

When there are multiple Booleans in a row of the alternatives grid, the solver deduces that the intersection of the alternative terms cannot be true:

Bob is either third, drinking apple juice, or wearing a blue jersey.

So the third one doesn’t have a blue jersey, the third one doesn’t drink apple juice, the blue jersey doesn’t drink apple juice.

Booleans that are in the alternatives grid, but not found in the zebra puzzle,  are removed from the alternatives grid .

If there is only one simple Boolean left in a row of the alternatives grid, it is replaced by a true sign in the puzzle. It then disappears from the alternatives grid. This is logical: if an alternative only includes one term… the solver considers that the latter is true, necessarily…