https://mediawiki.zeropage.org/index.php?action=history&feed=atom&title=The_Tower_of_Hanoi The Tower of Hanoi - Revision history 2026-05-14T16:20:25Z Revision history for this page on the wiki MediaWiki 1.39.8 https://mediawiki.zeropage.org/index.php?title=The_Tower_of_Hanoi&diff=85039&oldid=prev Maintenance script: Repair batch-0003 pages from live compare 2026-03-27T00:29:12Z <p>Repair batch-0003 pages from live compare</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:29, 27 March 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Recurrent Problems - The Tower of Hanoi ====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Recurrent Problems - The Tower of Hanoi ====</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>n<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>is the minimum number of moves that will transfer n disks from one peg to another under Lucas&#039;s rules.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>n<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>is the minimum number of moves that will transfer n disks from one peg to another under Lucas&#039;s rules.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===== small cases =====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===== small cases =====</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>0<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>= 0,  T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>1<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>= 1,  T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>2<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>= 3 .....</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>0<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>= 0,  T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>1<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>= 1,  T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>2<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>= 3 .....</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===== mathematical expression =====  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===== mathematical expression =====  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>0<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>= 0,  T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>n<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>= 2T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>n - 1<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>+ 1, for n &gt; 0&#039;&#039;&#039;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>0<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>= 0,  T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>n<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>= 2T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>n - 1<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>+ 1, for n &gt; 0&#039;&#039;&#039;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===== closed form =====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===== closed form =====</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;T<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sub<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>n<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sub<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>= 2<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>sup<del style="font-weight: bold; text-decoration: none;">&amp;gt;</del>n<del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>/sup<del style="font-weight: bold; text-decoration: none;">&amp;gt; </del>- 1, for n &gt;= 0&#039;&#039;&#039;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;T<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sub<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>n<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sub<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>= 2<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>sup<ins style="font-weight: bold; text-decoration: none;">&gt;</ins>n<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/sup<ins style="font-weight: bold; text-decoration: none;">&gt; </ins>- 1, for n &gt;= 0&#039;&#039;&#039;</div></td></tr> </table> Maintenance script https://mediawiki.zeropage.org/index.php?title=The_Tower_of_Hanoi&diff=39669&oldid=prev imported>Unknown at 05:28, 7 February 2021 2021-02-07T05:28:14Z <p></p> <p><b>New page</b></p><div>==== Recurrent Problems - The Tower of Hanoi ====<br /> T&amp;lt;sub&amp;gt;n&amp;lt;/sub&amp;gt; is the minimum number of moves that will transfer n disks from one peg to another under Lucas&#039;s rules.<br /> <br /> ===== small cases =====<br /> T&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt; = 0, T&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; = 1, T&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; = 3 .....<br /> <br /> ===== mathematical expression ===== <br /> &#039;&#039;&#039;T&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt; = 0, T&amp;lt;sub&amp;gt;n&amp;lt;/sub&amp;gt; = 2T&amp;lt;sub&amp;gt;n - 1&amp;lt;/sub&amp;gt; + 1, for n &gt; 0&#039;&#039;&#039;<br /> <br /> ===== closed form =====<br /> &#039;&#039;&#039;T&amp;lt;sub&amp;gt;n&amp;lt;/sub&amp;gt; = 2&amp;lt;sup&amp;gt;n&amp;lt;/sup&amp;gt; - 1, for n &gt;= 0&#039;&#039;&#039;</div> imported>Unknown