{"id":147,"date":"2023-08-01T14:46:23","date_gmt":"2023-08-01T12:46:23","guid":{"rendered":"https:\/\/actilud.com\/info\/en\/?p=147"},"modified":"2025-03-29T14:54:41","modified_gmt":"2025-03-29T13:54:41","slug":"merging","status":"publish","type":"post","link":"https:\/\/actilud.com\/info\/en\/merging\/","title":{"rendered":"Merging"},"content":{"rendered":"

Merging is the inverse of repercussion. The technique can find pivot cells that are false,<\/em> and, in some cases with Booleans, true cells <\/em>.<\/strong> Two rows can produce a false<\/strong> pivot cell if combining the two rows results in a false row.<\/p>\n

NB: You must have a good understanding of the repercussion technique before tackling this.<\/p>\n

By rotation\u2026<\/h1>\n

Let’s look at the example below:<\/p>\n

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Garry doesn’t drive for 30 minutes and an hour; as for the red yacht driver, he doesn’t drive for 20, 40, and 50 minutes. So the question is: Does Garry drive a red yacht?<\/p>\n

The answer is no,<\/em> of course, because if it were, he couldn’t drive for any of the times shown! Which isn’t possible, of course, since by definition, you need one true<\/em> sign per row.<\/p>\n

There’s a more visual way to figure this out. Let’s first find the pivot box:<\/p>\n

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It is (Garry, Red). But this time, when we perform a repercussion between the two grids, we obtain an impossible result:<\/p>\n

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Since this event cannot occur, the pivot box is therefore necessarily false:<\/p>\n

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By translation<\/h1>\n

What is true by rotation is also true, of course, by translation.<\/p>\n

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\nThe 14-year-old doesn’t drive for 30 minutes. If we translate the two columns, we realize that we get a column of false signs.<\/em><\/p>\n

Merging technique and Booleans<\/h1>\n

Find false boxes<\/h2>\n

Merging is even more interesting when it occurs with Booleans; if it shows a contradiction, then surely the pivot box is false.<\/p>\n

Let’s look at the -very simplified- example below:<\/p>\n

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First, notice that Chloe is driving either a blue yacht or a red yacht. Therefore, one of the two Booleans, a1 or a2, must be true, but they cannot both be true: a1 \u2260 a2<\/em><\/p>\n

Let’s ask ourselves the following question: can a 15-year-old drive for 40 minutes?<\/em><\/p>\n

If the answer is true,<\/em> then we have created a true pivot between the <\/em>15 years<\/em> and 40 min lines :<\/em><\/p>\n

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So, we need to mirror the two lines , which produces the superposition of<\/em> a1 and a2. This means that a1 = a2! But this contradicts what we already know. So the 15-year-old can’t drive for 40 minutes.<\/p>\n

And Chloe? Can she drive for 40 minutes? No, for the same reason.<\/p>\n

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You see that the merging technique gives particularly interesting results with Booleans.<\/p>\n

Find true boxes<\/h2>\n

Sometimes, the merging technique still allows us to discover true signs:<\/em><\/p>\n

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Does Rayan have a black yacht? The answer is yes!<\/em> Because if we superimpose the two rows corresponding to the pivot, we see that they are strictly identical.<\/em> So, regardless of the state of Booleans a1 and b1, we can safely say that yes, Rayan is indeed driving the black yacht!<\/p>\n

Note: this only works if each row has no empty boxes.<\/em><\/p><\/blockquote>\n

Find the pivot boxes<\/h1>\n

For the sake of simplicity, we will call “pivot” not only the boxes around which rotations are performed, but also those from which translations are performed – even if, strictly speaking, it is no longer really a “pivot”.<\/p>\n

By rotation<\/h2>\n

The pivot boxes by rotation are located on the central grids:<\/p>\n

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The central grids, in yellow.<\/figcaption><\/figure>\n

Here is where the peripheral grids are located when the central grid is first (Teen, Yacht):<\/p>\n

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Here is the rotation for the second grid (Teen, Duration):<\/p>\n

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Here is the third central grid, (Age, Yacht)<\/p>\n

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By translation, columns<\/h2>\n

The grid containing the pivot is always located below the left grid. The pivot box is at the intersection of the two column headers: (15 years, 30 minutes) for the first example.<\/p>\n

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By translation, lines<\/h2>\n

The pivot grid is always to the right of the top grid. The pivot box is at the intersection of the headers of the rows concerned; it is the box (Garry, 14 years old) in the first example.<\/p>\n

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