{"id":3500,"date":"2026-04-25T16:50:13","date_gmt":"2026-04-25T16:50:13","guid":{"rendered":"http:\/\/www.robertandrews.org\/LIFE\/?p=3500"},"modified":"2026-04-25T18:16:22","modified_gmt":"2026-04-25T18:16:22","slug":"five-card-finder","status":"publish","type":"post","link":"https:\/\/www.robertandrews.org\/LIFE\/five-card-finder\/","title":{"rendered":"Five Card Finder"},"content":{"rendered":"<h1><strong>Five Card Finder<\/strong><\/h1>\n<p><a href=\"http:\/\/www.robertandrews.org\/LIFE\/card-tricks\/\">RETURN TO CARD TRICK MENU<\/a><\/p>\n<hr \/>\n<ol>\n<li>Take any deck of cards and deal three piles of five cards each face down<\/li>\n<li>Set aside all other cards.\u00a0 They will not be used any more.<\/li>\n<li>Have The Mark pick any one of the piles, look at them all, and remember one card out of that pile<\/li>\n<li>Shuffle those cards together, and place them\u00a0ON TOP of one of the other piles<\/li>\n<li>Pick up the last 5 cards, and put that ON TOP of the pile of ten.<\/li>\n<li>Pick up all the cards without shuffling and deal out five piles of three cards each FACE UP.<\/li>\n<li>Ask The Mark which of the piles their card is in.<\/li>\n<li>Take that pile into your hand and put two of the other piles on the back side of the Mark&#8217;s cards<\/li>\n<li><span style=\"font-size: 12px;\"><strong>HINT: <\/strong>You can pick up the pile, then put the other two in the back, and place the cards face down.\u00a0 Pick up the remaining 6 cards and shuffle them and place them on the top of the pile.\u00a0 This will put the marks cards, in the middle of 6 cards on each side.<\/span><\/li>\n<li>Take that remaining two piles and shuffle them together.\u00a0 (Step 9)<\/li>\n<li>Pick up the fifteen cards without shuffling<\/li>\n<li>Deal the cards, face down, from left to right into two piles of ten each<\/li>\n<li>Discard all cards in the left pile<\/li>\n<li>Deal the cards, face down, from left to right into two piles<\/li>\n<li>Discard all cards in the left pile<\/li>\n<li>Deal the cards, face down, from left to right into two piles<\/li>\n<li>Discard the two cards in the left pile<\/li>\n<li>The remaining card is The Mark&#8217;s card<\/li>\n<\/ol>\n<input type='hidden' bg_collapse_expand='6a20283edb3f41094652132' value='6a20283edb3f41094652132'><input type='hidden' id='bg-show-more-text-6a20283edb3f41094652132' value='Claude&#039;s Analysis'><input type='hidden' id='bg-show-less-text-6a20283edb3f41094652132' value='Show Less'><button id='bg-showmore-action-6a20283edb3f41094652132' class='bg-showmore-plg-button bg-orange-button  '   style=\" color:#4a4949;\">Claude&#039;s Analysis<\/button><div id='bg-showmore-hidden-6a20283edb3f41094652132' >\n<h3 class=\"text-text-100 mt-2 -mb-1 text-base font-bold\">Phase 1: Sandwiching (Steps 1\u20135)<\/h3>\n<p class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\">The chosen pile gets placed <strong>between<\/strong> the other two, putting the mark&#8217;s card somewhere in <strong>positions 6\u201310<\/strong> of a 15-card stack.<\/p>\n<h3 class=\"text-text-100 mt-2 -mb-1 text-base font-bold\">Phase 2: The Dealing Revelation (Steps 6\u20137)<\/h3>\n<p class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\">Dealing 15 cards into 5 piles distributes them <strong>3 cards per pile, cyclically<\/strong>. Cards from positions 6\u201310 land as the <strong>middle card<\/strong> of each of the 5 piles. So no matter which pile the mark identifies, their card is always the <strong>2nd card of that pile<\/strong>.<\/p>\n<h3 class=\"text-text-100 mt-2 -mb-1 text-base font-bold\">Phase 3: Re-stacking to Position 8 (Steps 8\u201310)<\/h3>\n<ul class=\"[li_&amp;]:mb-0 [li_&amp;]:mt-1 [li_&amp;]:gap-1 [&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-disc flex flex-col gap-1 pl-8 mb-3\">\n<li class=\"whitespace-normal break-words pl-2\">Chosen pile (3 cards) on top of another pile \u2192 target card at <strong>position 2 of 6<\/strong><\/li>\n<li class=\"whitespace-normal break-words pl-2\">That 6 on top of last pile \u2192 target card at <strong>position 2 of 9<\/strong><\/li>\n<li class=\"whitespace-normal break-words pl-2\">The remaining 6 cards (two leftover piles) get shuffled and placed <strong>on top<\/strong> \u2192 target card is now at <strong>position 2+6 = 8 of 15<\/strong><\/li>\n<\/ul>\n<p class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\">This is the lock. The card is always at position 8, and in the right hand pile, regardless of which card, which pile, or any shuffle.<\/p>\n<h3 class=\"text-text-100 mt-2 -mb-1 text-base font-bold\">Phase 4: Binary Elimination (Steps 11\u201317)<\/h3>\n<p class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\">Dealing left-right and discarding left keeps only <strong>even-positioned cards<\/strong> each round:<\/p>\n<div class=\"overflow-x-auto w-full px-2 mb-6\">\n<table class=\"min-w-full border-collapse text-sm leading-[1.7] whitespace-normal\">\n<thead class=\"text-left\">\n<tr>\n<th class=\"text-text-100 border-b-0.5 border-border-300\/60 py-2 pr-4 align-top font-bold\" scope=\"col\">Round<\/th>\n<th class=\"text-text-100 border-b-0.5 border-border-300\/60 py-2 pr-4 align-top font-bold\" scope=\"col\">Cards<\/th>\n<th class=\"text-text-100 border-b-0.5 border-border-300\/60 py-2 pr-4 align-top font-bold\" scope=\"col\">Mark&#8217;s Position<\/th>\n<th class=\"text-text-100 border-b-0.5 border-border-300\/60 py-2 pr-4 align-top font-bold\" scope=\"col\">Lands in<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">1<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">15<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">8 (even)<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">Right \u2192 kept<\/td>\n<\/tr>\n<tr>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">2<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">7<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">4 (even)<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">Right \u2192 kept<\/td>\n<\/tr>\n<tr>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">3<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">3<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">2 (even)<\/td>\n<td class=\"border-b-0.5 border-border-300\/30 py-2 pr-4 align-top\">Right \u2192 <strong>sole survivor<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\">Position 8 = <strong>2\u00b3<\/strong> \u2014 a perfect power of two \u2014 so it survives exactly 3 rounds of halving. The math is inevitable.<\/p>\n<hr class=\"border-border-200 border-t-0.5 my-3 mx-1.5\" \/>\n<p class=\"font-claude-response-body break-words whitespace-normal leading-[1.7]\">The entire trick is essentially <strong>two funnels<\/strong>: the dealing phase guarantees the card is the middle of its pile, and the re-stacking converts &#8220;middle of 3&#8221; into position 8, which the binary deal then isolates perfectly.<\/p>\n<p><\/div><input type='hidden' bg_collapse_expand='6a20283edb61e0036974299' value='6a20283edb61e0036974299'><input type='hidden' id='bg-show-more-text-6a20283edb61e0036974299' value='Gemini&#039;s Analysis'><input type='hidden' id='bg-show-less-text-6a20283edb61e0036974299' value='Show Less'><button id='bg-showmore-action-6a20283edb61e0036974299' class='bg-showmore-plg-button bg-orange-button  '   style=\" color:#4a4949;\">Gemini&#039;s Analysis<\/button><div id='bg-showmore-hidden-6a20283edb61e0036974299' ><\/p>\n<p data-path-to-node=\"0\">This trick is a classic example of a <b data-path-to-node=\"0\" data-index-in-node=\"37\">positional elimination<\/b> or <b data-path-to-node=\"0\" data-index-in-node=\"63\">self-working mathematical card trick<\/b>. It relies on the precise tracking of a subset of cards through a series of &#8220;piles&#8221; to ensure the target card always ends up in a specific numerical position.<\/p>\n<p data-path-to-node=\"1\">Here is the breakdown of why the mechanics work:<\/p>\n<h3 data-path-to-node=\"2\">1. The Stacking Logic (Establishing Position)<\/h3>\n<p data-path-to-node=\"3\">By placing the chosen pile (containing the target card) between the other two piles, you are performing a <b data-path-to-node=\"3\" data-index-in-node=\"106\">sandwiching technique<\/b>.<\/p>\n<ul data-path-to-node=\"4\">\n<li>\n<p data-path-to-node=\"4,0,0\">Piles 2 and 3 each have 5 cards.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"4,1,0\">By putting the chosen pile on top of one and the other on top of that, the chosen 5 cards are now located at <b data-path-to-node=\"4,1,0\" data-index-in-node=\"109\">positions 6 through 10<\/b> in a 15-card stack.<\/p>\n<\/li>\n<\/ul>\n<h3 data-path-to-node=\"5\">2. The Deal (Redistributing)<\/h3>\n<p data-path-to-node=\"6\">When you deal the cards face up into 5 piles, you are essentially performing a <b data-path-to-node=\"6\" data-index-in-node=\"79\">modular distribution<\/b>. Since there are 15 cards and 5 piles:<\/p>\n<ul data-path-to-node=\"7\">\n<li>\n<p data-path-to-node=\"7,0,0\">Pile 1 gets cards 1, 6, 11.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"7,1,0\">Pile 2 gets cards 2, 7, 12.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"7,2,0\">Pile 3 gets cards 3, <b data-path-to-node=\"7,2,0\" data-index-in-node=\"21\">8<\/b>, 13.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"7,3,0\">Pile 4 gets cards 4, 9, 14.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"7,4,0\">Pile 5 gets cards 5, 10, 15.<\/p>\n<\/li>\n<\/ul>\n<p data-path-to-node=\"8\">Notice that the &#8220;target group&#8221; (original positions 6-10) is now distributed so that <b data-path-to-node=\"8\" data-index-in-node=\"84\">exactly one card from that group is in each of the 5 new piles.<\/b> Specifically, they are all the middle cards (the 2nd card dealt) of their respective 3-card piles.<\/p>\n<h3 data-path-to-node=\"9\">3. The Re-Stacking (The &#8220;Lock&#8221;)<\/h3>\n<p data-path-to-node=\"10\">When &#8220;The Mark&#8221; points to their pile, you know their card is the <b data-path-to-node=\"10\" data-index-in-node=\"65\">middle card<\/b> of that specific 3-card pile. By placing that pile on top of another pile of 3, and then placing that pile of 6 on top of the last pile of 3, you have moved the target card to <b data-path-to-node=\"10\" data-index-in-node=\"253\">position 5<\/b> in a 9-card stack.<\/p>\n<blockquote data-path-to-node=\"11\">\n<p data-path-to-node=\"11,0\"><b data-path-to-node=\"11,0\" data-index-in-node=\"0\">Note:<\/b> The trick instructions mention shuffling the &#8220;remaining two piles&#8221; (the cards not in the 15-card stack) and putting them on top. This is a &#8220;convincer&#8221;\u2014it adds bulk to the deck (bringing it back to a larger number) but doesn&#8217;t change the fact that the target card is now at a fixed, known depth from the top (usually <b data-path-to-node=\"11,0\" data-index-in-node=\"322\">position 8<\/b> if you include the 3 cards from the &#8220;other&#8221; pile and the 5 &#8220;extra&#8221; cards).<\/p>\n<\/blockquote>\n<h3 data-path-to-node=\"12\">4. The Binary Parity (Elimination)<\/h3>\n<p data-path-to-node=\"13\">The final phase uses <b data-path-to-node=\"13\" data-index-in-node=\"21\">Successive Elimination<\/b> (specifically a &#8220;reverse Australian deal&#8221;). By dealing into two piles and discarding the left one, you are mathematically narrowing the field:<\/p>\n<div class=\"horizontal-scroll-wrapper\">\n<div class=\"table-block-component\">\n<div class=\"table-block has-export-button new-table-style is-at-scroll-start is-at-scroll-end\">\n<div class=\"table-content not-end-of-paragraph\" data-hveid=\"0\" data-ved=\"0CAAQ3ecQahcKEwigppHs6dyTAxUAAAAAHQAAAAAQIw\">\n<table data-path-to-node=\"14\">\n<thead>\n<tr>\n<th><span data-path-to-node=\"14,0,0,0\">Round<\/span><\/th>\n<th><span data-path-to-node=\"14,0,1,0\">Cards Remaining<\/span><\/th>\n<th><span data-path-to-node=\"14,0,2,0\">Mechanism<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"14,1,0,0\"><b data-path-to-node=\"14,1,0,0\" data-index-in-node=\"0\">Initial<\/b><\/span><\/td>\n<td><span data-path-to-node=\"14,1,1,0\">15 (plus extras)<\/span><\/td>\n<td><span data-path-to-node=\"14,1,2,0\">Target is at a specific &#8220;power of 2&#8221; position.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"14,2,0,0\"><b data-path-to-node=\"14,2,0,0\" data-index-in-node=\"0\">Deal 1<\/b><\/span><\/td>\n<td><span data-path-to-node=\"14,2,1,0\">7-8 cards left<\/span><\/td>\n<td><span data-path-to-node=\"14,2,2,0\">You discard all &#8220;odd&#8221; positions (<span class=\"math-inline\" data-math=\"1, 3, 5...\" data-index-in-node=\"33\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">5&#8230;<\/span><\/span><\/span><\/span><\/span>).<\/span><\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"14,3,0,0\"><b data-path-to-node=\"14,3,0,0\" data-index-in-node=\"0\">Deal 2<\/b><\/span><\/td>\n<td><span data-path-to-node=\"14,3,1,0\">3-4 cards left<\/span><\/td>\n<td><span data-path-to-node=\"14,3,2,0\">You discard the new &#8220;odd&#8221; positions.<\/span><\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"14,4,0,0\"><b data-path-to-node=\"14,4,0,0\" data-index-in-node=\"0\">Deal 3<\/b><\/span><\/td>\n<td><span data-path-to-node=\"14,4,1,0\">1 card left<\/span><\/td>\n<td><span data-path-to-node=\"14,4,2,0\">The final remaining card.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"table-footer hide-from-message-actions\"><button class=\"mdc-button mat-mdc-button-base export-sheets-button-container mat-mdc-button mat-unthemed ng-star-inserted\"><span class=\"mdc-button__label\"><span class=\"export-sheets-button\">Export to Sheets<\/span><\/span><\/button><button class=\"mdc-icon-button mat-mdc-icon-button mat-mdc-button-base mat-mdc-tooltip-trigger copy-button mat-unthemed ng-star-inserted\" aria-label=\"Copy table\" data-test-id=\"copy-table-button\"><\/button><\/div>\n<\/div>\n<\/div>\n<\/div>\n<p data-path-to-node=\"15\">Because the target card was moved to a specific position during the &#8220;Which pile?&#8221; phase, the &#8220;Left-Right&#8221; deal acts as a <b data-path-to-node=\"15\" data-index-in-node=\"121\">sieve<\/b>. Every time you discard the left pile, you are discarding cards in positions <span class=\"math-inline\" data-math=\"2n-1\" data-index-in-node=\"204\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>. The math ensures that the target card&#8217;s position is never an &#8220;odd&#8221; position until it is the only one left.<\/p>\n<p><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Five Card Finder RETURN TO CARD TRICK MENU Take any deck of cards and deal three piles of five cards each face down Set aside all other cards.\u00a0 They will not be used any more. Have The Mark pick any one of the piles, look at them all, and remember [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21],"tags":[],"class_list":["post-3500","post","type-post","status-publish","format-standard","hentry","category-entertainment"],"_links":{"self":[{"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/posts\/3500","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/comments?post=3500"}],"version-history":[{"count":13,"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/posts\/3500\/revisions"}],"predecessor-version":[{"id":3539,"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/posts\/3500\/revisions\/3539"}],"wp:attachment":[{"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/media?parent=3500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/categories?post=3500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.robertandrews.org\/LIFE\/wp-json\/wp\/v2\/tags?post=3500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}