A complicated card trick that deals with the colors of the cards and a binary De Bruijn wheel has helped a mathematician reach a newfangled bandage on data compression . Magic and math , more favorable than you ’d think !
Here ’s how the caper works : You hand your friend a deck of cards and inquire them to string six add-in ( in order ) and name the colors . With that sequence of colors , you’re able to immediately name the exact cards that have been thread . How ? Because each color succession is unequaled and seem only once throughout the pack of cards ( after pre - arrange it to be so ) , so if you have an insane memory , you ’ll know which card correspond to the sequence .
According to Travis Gagie from the University of Chile in Santiago , the trick is intimately interrelate to data compression :
Gagie achieves this new [ mathematical ] constipate by considering a related whoremonger . or else of pre - set up the carte du jour , you scuffle the pack and then ask your friend to line seven menu . He or she then lists the cards ’ colours , supplant them in the pack and cuts the deck . You then try out the deck of cards and say which cards were drawn . This time you ’re relying on chance to get the right answer . “ It is not hard to show that the chance of two septuples of cards make the same colour in the same order is at most 1/128 , ”
This turns out to be closely related to various problems of data densification and leads to a lower bound than has been base by any other mean value .
illusionist as mathematicians , I should have known . [ Technology Review ]
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