k014's parametric magic cards

This is a parametric set of cards (quantity of card can be configured) that allow the owner to do a simple but amazing magic trick, here are the details:

Example Routine

• The magician ask the spectator to think in a number between 1 and N (N is configurable)
• Once the spectator is done, the magician handles all cards to the spectator
• The magician ask the spectator: "Please hand me all cards in which your number appears"
• Then, once the cards are separated, the magician ask for all rest of cards
• Then the magician take a quick look to the cards saying it will quickly see which number is missing from the rest pile
• Then the magician announces: "I see, the only number missing in the rest pile is number X!"
• The spectator, amazed, and the magician donates to the creator of this thing :)

Explanation

Of course, the previous example routine, is just an example, and the steps can be made in the order you want or change it as you like, what is important is to not reveal the secret:

Secret

Each card has a number in the top left corner, which you need to sum agains all card where the number appears, for example, if you are given 3 cards which corner numbers that are [1,4,8], then the number the sepectator thought was 1+4+8 = 13, simple right?

Why it works?

well, if you know how binary numbers work, each number in binary can be represented by a string of zeros and ones, for example, the first 4 numbers in binary are (check the pattern)

0001 = 1 0010 = 2 0011 = 3 0100 = 4 as you can see, each number is a specific combination of 0's and 1's, same as decimal system, in which each number is a combination of 10 digits (0 to 9), with that known, a 0 can be represented as "not present" and 1 can be "present", or in our case "number NOT present in card", "number present in card", this means for example:

0101 = 5 you will be given only 2 cards:

0001 = 1 +0100 = 4 -------------- 0101 = 5 then, the sum of the corners 1+4 = 5, the number the spectator thought

Algorithm

I created a python script to generate the magical cards based in how many cards you want to have, in the STL provided in this thing, I configured the script for 7 cards, but it will work with any number of card, for example, if you select 2 cards, it will generate the following cards:

[1, 3] [2, 3] an then you will only be able to guess numbers from 1 to 3, wanna try?, here are the possible combinations:

the spectator says his number appears in this cards:
[1,3]
result
the number is 1, summing the corner numbers: 1

the spectator says his number appears in this cards:
[2,3]
result
the number is 2, summing the corner numbers: 2

the spectator says his number appears in this cards:
[1,3]
[2,3]
result
the number is 3, summing the corner numbers: 1+2=3

and the are no other combination possible for the range 1 to 3, simple uh?

Try before you print!

check this image with all cards generated using 7 as input (then 7 cards generated)

• think in a number between 1 and 127, you got it?, cool
• sum the top left corner of each card in which that number appears
• voila!, it has to be your number :)

Printing Recomendations

This cards were designed to be printable using multicolor gcodes, you dont need to have a multi color printer, you just need to add a pause in the gcode in order to change filament color during print, I am using "color print" tool from prusaprinters.org, but there are tons of tutorials in youtube, I printed my last 2 cards in black just to see how they look, no need to do the same :D

• https://www.prusaprinters.org/color-print/

As always all my designs are opensource, since is code, I dont want to push code in thingverse because I want people to improve it and send me pull requests or if I do any change you will always download the latest version, here it is:

https://github.com/joecabezas/python-magic-cards

Dependencies:

• https://github.com/SolidCode/SolidPython
• Openscad

Category: Games