{"id":89,"date":"2023-08-01T10:55:27","date_gmt":"2023-08-01T08:55:27","guid":{"rendered":"https:\/\/actilud.com\/info\/en\/?p=89"},"modified":"2025-03-29T17:23:59","modified_gmt":"2025-03-29T16:23:59","slug":"gap-instruction","status":"publish","type":"post","link":"https:\/\/actilud.com\/info\/en\/gap-instruction\/","title":{"rendered":"The GAP instruction"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-808 alignleft\" src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/icone_pivot.png\" sizes=\"auto, (min-width: 960px) 75vw, 100vw\" srcset=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/icone_pivot.png 200w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/icone_pivot-150x150.png 150w\" alt=\"\" width=\"73\" height=\"73\" data-src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/icone_pivot.png\" data-srcset=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/icone_pivot.png 200w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/icone_pivot-150x150.png 150w\" data-sizes=\"(min-width: 960px) 75vw, 100vw\" \/>Create a gap between two items a and b using a regular ordered series.<\/p>\n<p>To use it, you therefore need at least one regular ordered series.<\/p>\n<p>To make solving easier, Booleans are recommended. This is one of the most complex instructions in zebra puzzles.<\/p>\n<h6>Ordered series: A series containing values \u200b\u200bthat are all increasing or all decreasing.<br \/>\nRegular ordered series: An increasing or decreasing series whose values \u200b\u200bare separated by the same interval.<\/h6>\n<blockquote>\n<h4>Land Yacht Riddle<\/h4>\n<p>There&#8217;s a three-year age gap between Lucas and the teenager driving the green yacht.<br \/>\nThere&#8217;s a 20-minute age gap between the person driving the blue yacht and the 17-year-old.<\/p><\/blockquote>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-2491\" src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart.png\" sizes=\"auto, (min-width: 960px) 75vw, 100vw\" srcset=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart.png 912w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-300x300.png 300w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-150x150.png 150w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-768x766.png 768w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-481x480.png 481w\" alt=\"\" width=\"912\" height=\"910\" data-src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart.png\" data-srcset=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart.png 912w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-300x300.png 300w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-150x150.png 150w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-768x766.png 768w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/ecart-481x480.png 481w\" data-sizes=\"(min-width: 960px) 75vw, 100vw\" \/><\/p>\n<p>The red and blue lines represent the relationships between the boxes across the grids, materialized by the Booleans.<\/p>\n<h4>Red line<\/h4>\n<p>If Lucas is 13, the green yacht driver is 16, and vice versa.<br \/>\nIf Lucas is 14, the green yacht driver is 17, and vice versa.<br \/>\nIf Lucas is 16, the green yacht driver is 13, and vice versa.<br \/>\nIf Lucas is 17, the green yacht driver is 14, and vice versa.<br \/>\nWhere we see that neither Lucas nor the green yacht driver can be 15, because 15-3=12, which is out of bounds, and 15+3=18, which is also out of bounds.<\/p>\n<h4>Blue line<\/h4>\n<p>Using the alternatives grid is essential to avoid losing information. It indicates that the 6 Booleans b1\u2026b6 form an alternative.<\/p>\n<p>If the driver of the blue yacht drives for 30 minutes, the 17-year-old drives for 50 minutes, and vice versa.<br \/>\nIf the driver of the blue yacht drives for 50 minutes, the 17-year-old drives for 30 minutes, and vice versa.<\/p>\n<p>Using the central space in both rows and the booleans b1, b6 and b3, b4:<\/p>\n<p>If the driver of the blue yacht drives for 20 minutes or for 1 hour, the 17-year-old drives for 40 minutes, and vice versa.<br \/>\nIf the 17-year-old drives for 20 minutes or for 1 hour, the driver of the blue yacht drives for 40 minutes, and vice versa.<\/p>\n<h3>False signs<\/h3>\n<p>Those present in the Boolean rows indicate positions that are outside the limit. We also discover <em>false<\/em><br \/>\nsigns at the intersection of the rows: Lucas cannot drive the green yacht, and the 17-year-old teenager cannot drive the blue yacht.<\/p>\n<h1>Designer<\/h1>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-823 size-full\" src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/integramme11.png\" sizes=\"auto, (min-width: 960px) 75vw, 100vw\" srcset=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/integramme11.png 314w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/integramme11-300x64.png 300w\" alt=\"\" width=\"314\" height=\"67\" data-src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/integramme11.png\" data-srcset=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/integramme11.png 314w, https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/integramme11-300x64.png 300w\" data-sizes=\"auto, (min-width: 960px) 75vw, 100vw\" \/><\/p>\n<p>Randomly chooses a regular ordered series D, two items a and b that refer to it, and a gap |i| between the two items. This gap is an absolute value: it goes in both directions (+i, -i).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-721 alignleft\" src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/sautcase.png\" alt=\"\" width=\"36\" height=\"35\" data-src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/sautcase.png\" \/><\/p>\n<p>The <em>jump<\/em> is the distance that must be specified <em>in number of boxes<\/em> that separate two items in each row. The jump will be converted to series-specific units (years, minutes, etc.) when generating formal propositions. The value of 0 gives a random choice. If n is the number of boxes per row, for a jump to be calculable, the minimum must be <span class=\"ILfuVd\" lang=\"fr\"><span class=\"hgKElc\"><b>\u230an\/2\u230b\u00a0<\/b><\/span><\/span><span class=\"ILfuVd\" lang=\"fr\"><span class=\"hgKElc\"> and the maximum <\/span><\/span><span class=\"ILfuVd\" lang=\"fr\"><span class=\"hgKElc\"><strong>n-2.<\/strong><\/span><\/span><span class=\"ILfuVd\" lang=\"fr\"><span class=\"hgKElc\"> That is, a value between 2 and 3 for a row of 5 boxes.<\/span><\/span><span class=\"ILfuVd\" lang=\"fr\"><span class=\"hgKElc\"> <b><\/b><br \/>\n<\/span><\/span><\/p>\n<h6><span class=\"ILfuVd\" lang=\"fr\"><span class=\"hgKElc\"> <b>\u230an\/2\u230b<\/b><\/span><\/span> means: integer part of n\/2<\/h6>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-687 alignleft\" src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/isole.png\" alt=\"\" width=\"35\" height=\"35\" data-src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/isole.png\" \/><\/p>\n<p>Isolated: If the instruction operates in isolated mode, the designer does not select rows that already contain signs, including Booleans.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-688 alignleft\" src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/maximum.png\" alt=\"\" width=\"35\" height=\"35\" data-src=\"https:\/\/actilud.com\/info\/wp-content\/uploads\/2023\/08\/maximum.png\" \/><\/p>\n<p>Maximum number of executions of this instruction.<\/p>\n<h2>Formal proposal generated<\/h2>\n<blockquote><p>D: \u0394(a,b) = \u00b1 i<br \/>\nthe gap in D between a and b is i<br \/>\nAge: \u0394 (Lucas, Green) = \u00b1 3<br \/>\nDuration: \u0394 (Blue, 17 years) = \u00b1 20<\/p><\/blockquote>\n<h6>D: header of the shared series containing a regular ordering relationship.<br \/>\na,b,: items using D<br \/>\n\u00b1 i,: value of the intervals, <em>in units of D;<\/em> i is applied in positive <em>and<\/em> negative because it is a gap.<\/h6>\n<h6><\/h6>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Create a gap between two items a and b using a regular ordered series. To use it, you therefore need at least one regular ordered series. To make solving easier, Booleans are recommended. This is one of the most complex instructions in zebra puzzles. Ordered series: A series containing values \u200b\u200bthat are all increasing or [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-89","post","type-post","status-publish","format-standard","hentry","category-zebra-puzzles-glossary-of-programming-instructions"],"_links":{"self":[{"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/posts\/89","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/comments?post=89"}],"version-history":[{"count":5,"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/posts\/89\/revisions"}],"predecessor-version":[{"id":113,"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/posts\/89\/revisions\/113"}],"wp:attachment":[{"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/media?parent=89"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/categories?post=89"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/actilud.com\/info\/en\/wp-json\/wp\/v2\/tags?post=89"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}