<?xml version="1.0" encoding="UTF-8" standalone="yes"?><oembed><version><![CDATA[1.0]]></version><provider_name><![CDATA[Chaos at the Sky]]></provider_name><provider_url><![CDATA[https://chaosatthesky.wordpress.com]]></provider_url><author_name><![CDATA[chaotic_iak]]></author_name><author_url><![CDATA[https://chaosatthesky.wordpress.com/author/chaoticiak/]]></author_url><title><![CDATA[Puzzle 75: TomTom is&nbsp;NP-complete]]></title><type><![CDATA[link]]></type><html><![CDATA[<p>This post has two puzzles!</p>
<p><b>Latin Square</b> Put an integer between 1 and the length of the grid (5) inclusive such that each row/column has each number exactly once.</p>
<p><b>Expected difficulty</b> <span style="color:#0000ff;">Easy</span> • <a href="https://dl.dropboxusercontent.com/u/32050066/Chaos%20at%20the%20Sky/Answers/075a.png">Answer</a> • <span style="color:#800000;">Comment/E-mail if you want a solution to be published</span></p>
<div data-shortcode="caption" id="attachment_1379" style="width: 173px" class="wp-caption aligncenter"><a href="https://chaosatthesky.files.wordpress.com/2014/01/075a-latin-square.png"><img loading="lazy" aria-describedby="caption-attachment-1379" data-attachment-id="1379" data-permalink="https://chaosatthesky.wordpress.com/2014/01/07/p075/075a-latin-square/" data-orig-file="https://chaosatthesky.files.wordpress.com/2014/01/075a-latin-square.png" data-orig-size="163,163" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}" data-image-title="075a &#8211; Latin Square" data-image-description="" data-image-caption="&lt;p&gt;Puzzle 75: TomTom is NP-complete&lt;br /&gt;
Latin Square&lt;/p&gt;
" data-medium-file="https://chaosatthesky.files.wordpress.com/2014/01/075a-latin-square.png?w=163" data-large-file="https://chaosatthesky.files.wordpress.com/2014/01/075a-latin-square.png?w=163" src="https://chaosatthesky.files.wordpress.com/2014/01/075a-latin-square.png?w=163&#038;h=163" alt="Puzzle 75a: Latin Square" width="163" height="163" class="size-full wp-image-1379" srcset="https://chaosatthesky.files.wordpress.com/2014/01/075a-latin-square.png 163w, https://chaosatthesky.files.wordpress.com/2014/01/075a-latin-square.png?w=150&amp;h=150 150w" sizes="(max-width: 163px) 100vw, 163px" /></a><p id="caption-attachment-1379" class="wp-caption-text">Puzzle 75: TomTom is NP-complete<br />Latin Square</p></div>
<p><b>TomTom</b> Put an integer between 1 and the length of the grid (10) inclusive such that each row/column has each number exactly once. The number at the top-left of each region indicates the value of a mathematical operation (addition, subtraction, multiplication, division) applied successively to all digits in the cage, starting with the largest digit for subtraction and division (e.g. 1,2,4 with subtraction is a 1- clue as 4-2-1 = 1). (Description from <a href="http://www.gmpuzzles.com/blog/tomtom-rules-and-info/">Grandmaster Puzzles</a>)</p>
<p><b>Expected difficulty</b> <span style="color:#0000ff;">Easy</span> • <a href="https://dl.dropboxusercontent.com/u/32050066/Chaos%20at%20the%20Sky/Answers/075b.png">Answer</a> • <span style="color:#800000;">Comment/E-mail if you want a solution to be published</span></p>
<div data-shortcode="caption" id="attachment_1380" style="width: 333px" class="wp-caption aligncenter"><a href="https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png"><img loading="lazy" aria-describedby="caption-attachment-1380" data-attachment-id="1380" data-permalink="https://chaosatthesky.wordpress.com/2014/01/07/p075/075b-tomtom/" data-orig-file="https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png" data-orig-size="323,323" data-comments-opened="1" data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}" data-image-title="075b &#8211; TomTom" data-image-description="" data-image-caption="&lt;p&gt;Puzzle 75: TomTom is NP-complete&lt;br /&gt;
TomTom&lt;/p&gt;
" data-medium-file="https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png?w=300" data-large-file="https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png?w=323" src="https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png?w=323&#038;h=323" alt="Puzzle 75b: TomTom" width="323" height="323" class="size-full wp-image-1380" srcset="https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png 323w, https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png?w=150&amp;h=150 150w, https://chaosatthesky.files.wordpress.com/2014/01/075b-tomtom.png?w=300&amp;h=300 300w" sizes="(max-width: 323px) 100vw, 323px" /></a><p id="caption-attachment-1380" class="wp-caption-text">Puzzle 75: TomTom is NP-complete<br />TomTom</p></div>
<p>I guess the two puzzles above prove that TomTom is NP-complete. We can see a trivial polynomial transformation from a Latin Square to a TomTom, and <a href="www.sciencedirect.com/science/article/pii/0166218X84900751">Latin Square is NP-complete</a>.</p>
<p>So, <a href="https://chaosatthesky.wordpress.com/2014/01/05/np-complete-g-and-p/#comment-502">sorry for Jacob Lance</a>.</p>
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