Two magicians A and B perform the following trick:

A leaves the room and B chooses 4 members from the audience at random. Each member chooses a card numbered from 1 to 100 (each chooses a different card) and after B has seen their cards he chooses a card from the remaining deck of cards. The 5 chosen cards are shuffled by an audience member and handed to A who just returned to the room. Prove that A is able to figure out which cards each member picked. Consider that the chosen members form a row and e.g. the leftmost member picks the first card and the rightmost member (B) picks the last card.

(In reply to please read by Charlie)

Charle

Any 5  different  numbers between 1 and 100 inclusive  enable an unique extraction of B's  number and using this number to evaluate to correctly assign the remaining 4 numbers to the coorrect persons.,provided one of the numbers was introduced by B by an algorythm previously agreed upon

In my version 1,2,3,4,5  B's number is 5 and 1234 ==>CDEF

If it were 1,2,3,4,28  B's number is 24 and 1234 ==>FEDC

If it were 1,2,3,4,55   A would say "what's wrong with you, my dear B"   or use common sense   and  declare (since  A55 mod 24=7) :1234 ==>DCFE

 

Please comment

Posted by Ady TZIDON on 2007-05-12 14:16:37