# Cunning Card Trick a solution 1

Download 8.88 Kb.
 Date conversion 28.08.2017 Size 8.88 Kb.
 Cunning Card Trick – A Solution 1st May 2007 Solution provided by Alexander Gunasekera and James Currah, both year 5 pupils of The Batt Primary School, Witney At the end of the trick, let the three chosen piles be called pile A, pile B and pile M. The remaining cards are in the magic pile P. Pile A and Pile B are the two piles revealed at the end, pile M is the mystery pile. We know the values of A and B (eg ace is 1, 2 is 2 ... Jack is 11 and so on) as A and B are the values of the bottom cards revealed. We do not know the card M. We want to find M out. Let the number of cards in pile A be nA. Let the number of cards in pile B be nB. Let the number of cards in pile M be nM. Let the number of cards in pile P be nP. We know what nP is because we can count the cards in the magic pile. Take the pile A for example: If the bottom card is 5 then there are 9 cards in the pile (5, 6, 7, 8, 9, 10, J, Q, K). If the bottom card is J (11) then there are 3 cards in the pile ( J, Q, K). Generally we can say that the number of cards in pile A (nA) is equal to 14 subtract the value of the bottom card, A. Or: nA = 14 – A Similarly, nB = 14 – B And nM = 14 – M We also know that there are 52 cards in a pack so we know: nA + nB + nM + nP = 52 Using the information above: 14 - A + 14 – B + 14 – M + nP =52 Tidying this up gives: 42 – A – B – M + nP = 52 Tidying again gives: nP – A – B – M = 10 and again gives M = nP – A – B – 10 Remember, M is the value of the mystery card we want to find. In the trick, to find M we count the number of cards in the magic pile, subtract A cards then subtract B cards then subtract 10 cards. The number of cards left is M. This works because we have shown that, M = nP – A – B – 10 above.

The database is protected by copyright ©hestories.info 2017
send message