<?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[Tiltmaze]]></title><type><![CDATA[link]]></type><html><![CDATA[<p>Tiltmaze is a series of puzzles. They are much better played interactively, but because I&#8217;m too lazy to make an applet for it, it&#8217;s going to be simply an image. You have to imagine yourself. They are also in some sense optimization.</p>
<p>The objective is to bring all the &#8220;balls&#8221; to the &#8220;goals&#8221;. However, you won&#8217;t be controlling them directly. You will tilt the entire grid to one of the four cardinal directions every move; most objects move in that direction until they hit something and hence cannot move any more.</p>
<p><b>Attributes</b> (all of these might be overridden if specified such)<br />
&#8211; <i>Slides / Moves / Doesn&#8217;t move</i>: Every tilt, an object that &#8220;slides&#8221; will move in said direction until bumping to another object; an object that &#8220;moves&#8221; will move a specified number of squares in said direction unless it will bump in which it will move the most number of squares without bumping; an object that &#8220;doesn&#8217;t move&#8221;&#8230;doesn&#8217;t move, it stays perfectly still.<br />
&#8211; <i>Solid / Non-solid</i>: A &#8220;solid&#8221; object occupies space, and so by <a href="http://wiki.answers.com/Q/Who_said_that_no_two_objects_can_occupy_the_same_space_at_the_same_time">extension of Pauli exclusion principle</a> no two solid objects can phase through each other. This means two solid objects can &#8220;bump&#8221;. For example, a ball against a wall will stop at the cell right before phasing through the wall, and a ball against another (that is stationary) will stop right before going to occupy the same cell as the latter ball. No such thing happens with &#8220;non-solid&#8221; objects against anything.<br />
&#8211; <i>Cell / Border</i>: A &#8220;cell&#8221; object occupies a single cell. A &#8220;border&#8221; object occupies the border (unit segment) between two cells.</p>
<p><b>Objects</b><br />
<span style="text-decoration:underline;">Fundamental objects</span><br />
&#8211; Ball (green solid circle): An object that you should guide to the goal (see below). <i>Cell; slides; solid.</i><br />
&#8211; Goal (thin blue circle): The destination where a ball should be guided (see above); ball must be stationary in order to count. <i>Cell; doesn&#8217;t move; non-solid.</i></p>
<p><span style="text-decoration:underline;">Blockers</span><br />
&#8211; Wall (thin black border): An impenetrable wall; causes most objects to bump to them. <i>Border; doesn&#8217;t move; solid.</i><br />
&#8211; Cliff (black border with arrows): A one-sided wall. Objects coming from the&#8230;uh&#8230;&#8221;open&#8221; side phases through the cliff (jumps down), but objects coming from the &#8220;closed&#8221; side bumps to the cliff like it&#8217;s a wall. <i>Border; doesn&#8217;t move; somewhat solid (read ←).</i><br />
&#8211; Box (olive solid circle): A regular object, impenetrable. <i>Cell; slides; solid.</i></p>
<p><span style="text-decoration:underline;">Antagonists</span><br />
&#8211; Enemy (red solid circle): Bad thing, don&#8217;t touch. When a ball hit an enemy (or an enemy hit a ball), the ball is destroyed (and you lose). A ball and an enemy that are simply occupying adjacent cells don&#8217;t cause you to lose, but if one of them move toward each other (and there is no wall), it will still cause a hit and hence a loss. Acts as a regular object otherwise. <i>Cell; slides; solid.</i></p>
<p><b>Example</b><br />
<span style="text-decoration:underline;">Mechanics</span></p>
<div data-shortcode="caption" id="attachment_1179" style="width: 177px" class="wp-caption aligncenter"><a href="https://chaosatthesky.files.wordpress.com/2013/06/example-01a.png"><img loading="lazy" aria-describedby="caption-attachment-1179" data-attachment-id="1179" data-permalink="https://chaosatthesky.wordpress.com/puzzles/tiltmaze/example-01a/" data-orig-file="https://chaosatthesky.files.wordpress.com/2013/06/example-01a.png" data-orig-size="167,167" 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="Example 01a" data-image-description="" data-image-caption="&lt;p&gt;Example grid&lt;/p&gt;
" data-medium-file="https://chaosatthesky.files.wordpress.com/2013/06/example-01a.png?w=167" data-large-file="https://chaosatthesky.files.wordpress.com/2013/06/example-01a.png?w=167" class="size-full wp-image-1179" alt="Example grid" src="https://chaosatthesky.files.wordpress.com/2013/06/example-01a.png?w=167&#038;h=167" width="167" height="167" srcset="https://chaosatthesky.files.wordpress.com/2013/06/example-01a.png 167w, https://chaosatthesky.files.wordpress.com/2013/06/example-01a.png?w=150&amp;h=150 150w" sizes="(max-width: 167px) 100vw, 167px" /></a><p id="caption-attachment-1179" class="wp-caption-text">Example grid</p></div>
<p>The above is an example grid. You may use any number of moves to complete the objective, although it&#8217;s a neat secondary objective if you can match (or beat) my solution 🙂</p>
<p>So, here&#8217;s the above grid after the move ↑ (up):</p>
<div data-shortcode="caption" id="attachment_1180" style="width: 177px" class="wp-caption aligncenter"><a href="https://chaosatthesky.files.wordpress.com/2013/06/example-01b.png"><img loading="lazy" aria-describedby="caption-attachment-1180" data-attachment-id="1180" data-permalink="https://chaosatthesky.wordpress.com/puzzles/tiltmaze/example-01b/" data-orig-file="https://chaosatthesky.files.wordpress.com/2013/06/example-01b.png" data-orig-size="167,167" 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="Example 01b" data-image-description="" data-image-caption="&lt;p&gt;After move &amp;uarr;&lt;/p&gt;
" data-medium-file="https://chaosatthesky.files.wordpress.com/2013/06/example-01b.png?w=167" data-large-file="https://chaosatthesky.files.wordpress.com/2013/06/example-01b.png?w=167" class="size-full wp-image-1180" alt="After move ↑" src="https://chaosatthesky.files.wordpress.com/2013/06/example-01b.png?w=167&#038;h=167" width="167" height="167" srcset="https://chaosatthesky.files.wordpress.com/2013/06/example-01b.png 167w, https://chaosatthesky.files.wordpress.com/2013/06/example-01b.png?w=150&amp;h=150 150w" sizes="(max-width: 167px) 100vw, 167px" /></a><p id="caption-attachment-1180" class="wp-caption-text">After move ↑</p></div>
<p>The fastest solution to this puzzle can be easily proven to be 4 moves: ↑←↓→. (There also exists a solution with 7 moves →↑←↑←↓→, and you can easily extend any solution by including useless moves, such as inserting a → after the ↑ in the best solution.) Note that the 2-move sequence →↑ is not a solution, since the ball must stop right at the goal (and not simply passing it; in other words, winning condition is only checked between moves).</p>
<p><span style="text-decoration:underline;">Multiple objects</span></p>
<div data-shortcode="caption" id="attachment_1181" style="width: 177px" class="wp-caption aligncenter"><a href="https://chaosatthesky.files.wordpress.com/2013/06/example-02a.png"><img loading="lazy" aria-describedby="caption-attachment-1181" data-attachment-id="1181" data-permalink="https://chaosatthesky.wordpress.com/puzzles/tiltmaze/example-02a/" data-orig-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02a.png" data-orig-size="167,167" 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="Example 02a" data-image-description="" data-image-caption="&lt;p&gt;Example grid&lt;/p&gt;
" data-medium-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02a.png?w=167" data-large-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02a.png?w=167" class="size-full wp-image-1181" alt="Example grid" src="https://chaosatthesky.files.wordpress.com/2013/06/example-02a.png?w=167&#038;h=167" width="167" height="167" srcset="https://chaosatthesky.files.wordpress.com/2013/06/example-02a.png 167w, https://chaosatthesky.files.wordpress.com/2013/06/example-02a.png?w=150&amp;h=150 150w" sizes="(max-width: 167px) 100vw, 167px" /></a><p id="caption-attachment-1181" class="wp-caption-text">Example grid</p></div>
<p>Everything moves together, since you tilt the whole grid. So, after a move ↑, the grid looks as follows:</p>
<div data-shortcode="caption" id="attachment_1182" style="width: 177px" class="wp-caption aligncenter"><a href="https://chaosatthesky.files.wordpress.com/2013/06/example-02b.png"><img loading="lazy" aria-describedby="caption-attachment-1182" data-attachment-id="1182" data-permalink="https://chaosatthesky.wordpress.com/puzzles/tiltmaze/example-02b/" data-orig-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02b.png" data-orig-size="167,167" 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="Example 02b" data-image-description="" data-image-caption="&lt;p&gt;After move &amp;uarr;&lt;/p&gt;
" data-medium-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02b.png?w=167" data-large-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02b.png?w=167" class="size-full wp-image-1182" alt="After move ↑" src="https://chaosatthesky.files.wordpress.com/2013/06/example-02b.png?w=167&#038;h=167" width="167" height="167" srcset="https://chaosatthesky.files.wordpress.com/2013/06/example-02b.png 167w, https://chaosatthesky.files.wordpress.com/2013/06/example-02b.png?w=150&amp;h=150 150w" sizes="(max-width: 167px) 100vw, 167px" /></a><p id="caption-attachment-1182" class="wp-caption-text">After move ↑</p></div>
<p>Also, when a solid cell object bumps to another, the solid cell object stops at the cell right before the latter. So, if we move →, the grid looks as follows:</p>
<div data-shortcode="caption" id="attachment_1183" style="width: 177px" class="wp-caption aligncenter"><a href="https://chaosatthesky.files.wordpress.com/2013/06/example-02c.png"><img loading="lazy" aria-describedby="caption-attachment-1183" data-attachment-id="1183" data-permalink="https://chaosatthesky.wordpress.com/puzzles/tiltmaze/example-02c/" data-orig-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02c.png" data-orig-size="167,167" 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="Example 02c" data-image-description="" data-image-caption="&lt;p&gt;After moves &amp;uarr;&amp;rarr;&lt;/p&gt;
" data-medium-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02c.png?w=167" data-large-file="https://chaosatthesky.files.wordpress.com/2013/06/example-02c.png?w=167" class="size-full wp-image-1183" alt="After moves ↑→" src="https://chaosatthesky.files.wordpress.com/2013/06/example-02c.png?w=167&#038;h=167" width="167" height="167" srcset="https://chaosatthesky.files.wordpress.com/2013/06/example-02c.png 167w, https://chaosatthesky.files.wordpress.com/2013/06/example-02c.png?w=150&amp;h=150 150w" sizes="(max-width: 167px) 100vw, 167px" /></a><p id="caption-attachment-1183" class="wp-caption-text">After moves ↑→</p></div>
<p>The fastest solution to this puzzle is ↑←↑→↑, which utilizes a box at R1C4 so the ball, moving ↑, can stop at R2C4 and completing the puzzle.</p>
<p><b>Puzzles</b><br />
<span style="text-decoration:underline;">Tutorial Pack</span><br />
&#8211; <a href="https://chaosatthesky.wordpress.com/2013/06/02/tiltmaze001/">Tiltmaze 1: The Plains</a><br />
&#8211; <a href="https://chaosatthesky.wordpress.com/2013/06/03/tiltmaze002/">Tiltmaze 2: Divided By Two</a><br />
&#8211; <a href="https://chaosatthesky.wordpress.com/2013/06/04/tiltmaze003/">Tiltmaze 3: Sacrifices</a></p>
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