# Tends to infinity

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# Archive for the ‘combinatorics’ Category

## Who has taken what?

Posted by tendstoinfinity on January 17, 2011

pichak@scientist.com

I recently attended in-service training programme of teachers. There Dr. A N mishra of kendriya vidyalaya, ONGC Jorhat demonstrated a very beautiful magic to begin the chapter Permutation.  I am presenting the magic. Hope you’ll like it.

I have three friends say A, B, C whom I invited. They took my three important possession say my watch, ring and my pen one each when I was away from my room. When I returned to the room they told if I can correctly say “who has taken what?” then they would  return otherwise I should forget those three things!! I had 24 toffees( you can take any other thing like ground nut etc.)in my pocket. I gave one toffee to A, 2 toffees to B and 3 toffees to C and place the rest on the table. I told them “I am going out of the room, the person who taken watch should take same number of toffee as he has, the person with ring will take double of what he has and he with the pen will take four times of his possession.” I went out of the room and then returned and gazed the remaining toffees on the table. Hurray! I found who has taken what. Are you astonished? How did I find.

I simply wrote the total arrangement possibility and remember initially A has 1, B has 2 and C has 3 toffees.

 A B C Toffees taken Rest toffees W(1+1) R(2+4) P(3+12) 23 1 W(1+1) P(2+8) R(3+6) 21 3 R(1+2) W(2+2) P(3+12) 22 2 R(1+2) P(2+8) W(3+3) 19 5 P(1+4) W(2+2) R(3+6) 18 6 P(1+4) R(2+4) W(3+3) 17 7

hope you understood how I guessed by seeing  the rest number toffees.