<\/p>\n\n\n\n
I love this math principal. This version was in THE
“WORLD\u2019S BEST COLLECTION OF EAS Y-TO-DO IMPROMPTU CARD MAGIC” compiled by Aldo Colombini and published in 2003.<\/p>\n\n\n\n\n\n\n\n
A spectator’s freely chosen card automatically moves to the bottom of the deck through an apparently random shuffling procedure.<\/p>\n\n\n\n
Deal 24 cards to the table to make a packet. (You can do this openly as part of your patter about using “a smaller packet for better control.”) (Also, see my additional thoughts at the end.)<\/p>\n\n\n\n
Step 1: The Choice<\/strong> “I’d like you to think of any number between one and ten – don’t tell me what it is yet. This number represents how unpredictable you are as a person. Got one? Good.”<\/em><\/p>\n\n\n\n Step 2: The Deal<\/strong> “Now deal that many cards silently onto the table, one at a time. I’ll turn away so I can’t count along.”<\/em><\/p>\n\n\n\n Turn away while they deal. When they finish:<\/p>\n\n\n\n “Perfect! Now put those cards in your pocket – we won’t need them again. They represent the chaos you’ve introduced into our little experiment.”<\/em><\/p>\n\n\n\n Step 3: The Selection<\/strong> “Now, look at the card that’s at your chosen number from the top of the remaining cards. Don’t remove it, just remember it. This is your card – the one that reflects your unpredictable choice.”<\/em><\/p>\n\n\n\n Step 4: The “Shuffle”<\/strong> “I’m going to shuffle these cards in a very specific way – I call it the ‘chaos shuffle’ because it seems random but follows a precise pattern.”<\/em><\/p>\n\n\n\n Take the packet and move 6 cards from top to bottom, counting aloud: “Six cards from order to chaos…”<\/em><\/p>\n\n\n\n Repeat this three more times, each time saying:<\/p>\n\n\n\n Step 5: The Revelation<\/strong> “Your unpredictable choice, combined with this chaotic shuffle, should have created complete randomness. But sometimes, in the midst of chaos, perfect order emerges. What was your number?”<\/em><\/p>\n\n\n\n After they reveal their number: “And your card was…?”<\/em><\/p>\n\n\n\n Turn over the bottom card: “Sometimes the universe has a sense of humor about our attempts at randomness.”<\/em><\/p>\n\n\n\n You could frame this as a “mathematical destiny” effect, explaining how their personal choice combines with mathematical principles to create an inevitable outcome – playing up the self-working nature as something mystical rather than chaotic.Retry<\/p>\n\n\n\n Initial state<\/strong>: 24 cards total Spectator action<\/strong>: Removes N cards (where N = 1-10), leaving (24-N) cards Target card<\/strong>: Located at position N from the top of the remaining deck Performer action<\/strong>: Moves 6 cards from top to bottom, four times (24 cards total)<\/p>\n\n\n\n The magic happens because of this modular arithmetic relationship: 24 \u2261 N (mod (24-N))<\/strong><\/p>\n\n\n\n Here’s why this is true: 24 = 1\u00d7(24-N) + N, which means when we divide 24 by (24-N), the remainder is N.<\/p>\n\n\n\n When you move cards from top to bottom, you’re creating a cyclic shift. Moving 24 cards from top to bottom shifts every card’s position by -24 positions.<\/p>\n\n\n\n The target card starts at position N and moves to position: N – 24 \u2261 N – N \u2261 0 (mod (24-N))<\/strong><\/p>\n\n\n\n Since we use 1-based indexing, position 0 corresponds to the bottom position of the deck.<\/p>\n\n\n\n N = 3<\/strong>: Remaining deck has 21 cards, target at position 3<\/p>\n\n\n\n N = 7<\/strong>: Remaining deck has 17 cards, target at position 7<\/p>\n\n\n\n N = 10<\/strong>: Remaining deck has 14 cards, target at position 10<\/p>\n\n\n\n No matter which number N the spectator chooses (1-10), the mathematical relationship 24 \u2261 N (mod (24-N))<\/strong> ensures that moving exactly 24 cards will always place their selected card at the bottom of the remaining packet.<\/p>\n\n\n\n This is a perfect example of how modular arithmetic creates self-working magic!<\/p>\n\n\n\n For any packet of K<\/strong> cards, moving exactly K<\/strong> cards from top to bottom will place the selection on the bottom, regardless of which number N the spectator chooses.<\/p>\n\n\n\n This works because: K \u2261 N (mod (K-N))<\/strong> for any valid N<\/p>\n\n\n\n The mathematical relationship K = 1\u00d7(K-N) + N<\/strong> means that K divided by (K-N) always leaves remainder N.<\/p>\n\n\n\n N = 4<\/strong>: 26-4 = 22 cards remain, target at position 4<\/p>\n\n\n\n N = 8<\/strong>: 26-8 = 18 cards remain, target at position 8<\/p>\n\n\n\n N = 13<\/strong>: 26-13 = 13 cards remain, target at position 13<\/p>\n\n\n\n This creates a beautiful self-working<\/strong> system for any packet size:<\/p>\n\n\n\n The mathematics guarantees it works every single time, which is what makes this such an elegant and powerful principle in card magic!<\/p>\n\n\n\n If I am performing for magicians I deal out 26 cards instead of 24. Then when I do the first three cuts of six cards I actually do a little finger pull down on the two bottom cards of the packet and insert the six cards there. On the last transfer I really do put the six cards on the bottom resulting in the selection being on the bottom. Thus when the other magicians try to repeat the trick, they fail.<\/p>\n\n\n\n The four sets of six is just a suggestion. The trick works as long as you move 24 cards. So, for example you could use the sentence “your card is on the bottom now”, transfering blocks corresponding to the word lengths: 4, 4, 2, 2, 3, 6, and 3.<\/p>\n\n\n\n Take the Ace through 10 of mix suits, in order and place them after the 18th card in a deck. Now you can have the spectator cut the deck, “somewhere near the middle” and hand you the cut off cards. A quick glimpse of the bottom card tells you how many cards are in the packet. For example, say the card it the five. Five plus eighteen = 23. Now perform the trick.<\/p>\n\n\n\n Another option is to corner crimp the 26 or 27th card. Have the spectator cut off something just less than have the deck and shuffle those cards. By counting the cards above the crimped card you can tell how many cards the spectator has. For example, if the 27th card was crimped and you see five cards above the crimp you know they have 21 cards.<\/p>","protected":false},"excerpt":{"rendered":" I love this math principal. This version was in THE“WORLD\u2019S BEST COLLECTION OF EAS Y-TO-DO IMPROMPTU CARD MAGIC” compiled by Aldo Colombini and published in 2003.<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_eb_attr":"","footnotes":""},"categories":[7,1,159],"tags":[],"class_list":["post-7407","post","type-post","status-publish","format-standard","hentry","category-magic","category-miscellaneous","category-self-working"],"featured_image_src":null,"featured_image_src_square":null,"author_info":{"display_name":"Bob","author_link":"https:\/\/robertjwallace.com\/es\/author\/admin\/"},"_links":{"self":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts\/7407","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/comments?post=7407"}],"version-history":[{"count":5,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts\/7407\/revisions"}],"predecessor-version":[{"id":7416,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/posts\/7407\/revisions\/7416"}],"wp:attachment":[{"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/media?parent=7407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/categories?post=7407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/robertjwallace.com\/es\/wp-json\/wp\/v2\/tags?post=7407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Alternative Patter Theme<\/h2>\n\n\n\n
The Setup Analysis<\/h2>\n\n\n\n
The Mathematical Key<\/h2>\n\n\n\n
The Transformation<\/h2>\n\n\n\n
Examples<\/h2>\n\n\n\n
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The Elegant Result<\/h2>\n\n\n\n
The General Rule<\/h2>\n\n\n\n
Why This Always Works<\/h2>\n\n\n\n
Examples with 26 Cards<\/h2>\n\n\n\n
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The Universal Principle<\/h2>\n\n\n\n
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Additional thoughts<\/h2>\n\n\n\n
Additional Additional Thoughts<\/h2>\n\n\n\n