{"id":159,"date":"2023-08-01T15:56:08","date_gmt":"2023-08-01T13:56:08","guid":{"rendered":"https:\/\/actilud.com\/info\/en\/?p=159"},"modified":"2025-03-29T16:46:54","modified_gmt":"2025-03-29T15:46:54","slug":"alternatives","status":"publish","type":"post","link":"https:\/\/actilud.com\/info\/en\/alternatives\/","title":{"rendered":"The alternatives"},"content":{"rendered":"
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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.<\/p>\n

In a statement, alternatives are mutually exclusive propositions.<\/p>\n

Simple case: in a grid<\/h2>\n

Alice wears a blue, red or green swimsuit.<\/p><\/blockquote>\n

The expression\u00a0 or<\/em> corresponds to the exclusive or\u00a0<\/em> of mathematics: Alice wears either the blue jersey, or the red one, or the green one, but she does not wear multiple colors. Nor does she wear the other colors present in the grid.<\/p>\n

Reporting this statement in a grid is very simple:<\/p>\n

\"\"<\/p>\n

Where we see that Alice is wearing neither yellow nor white.<\/figcaption><\/figure>\n

Simply complete the row with false<\/em> signs in the boxes that are ignored.<\/p>\n

Complex case: on several grids<\/h2>\n

But an alternative can also relate to several grids:<\/p>\n

The first is either Bob or the red jersey.<\/p><\/blockquote>\n

Let’s analyze this sentence. Bob cannot wear a red jersey. Indeed, if Bob is first, then he cannot wear red. But if he is not first, then the red jersey wins, and so again Bob cannot wear red.<\/p>\n

To encode this situation in a grid, we need booleans.<\/p>\n

\"\"<\/p>\n

We need two different Booleans, for example a1<\/em> and a2<\/em> . To code the alternative, we place a1<\/em> at the intersection (Bob, 1) and a2<\/em> at the intersection (Red, 1). If we were working with a pencil and eraser, we would note in a corner of our paper that a1 and a2 form an alternative. On the site, we place a1 and a2 in the alternatives grid, in the same row, to indicate the alternative to the solver.<\/p>\n

To consider that two Booleans form an alternative is to assert that:<\/p>\n