Friday, January 18, 2008

Board to Reverse-Board

Here is a not-so-interesting Puzzle

Imagine a chess board with 64 squares.

Define a Board :

1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64

Define a Reverse-Board

64 63 62 61 60 59 58 57
56 55 54 53 52 51 50 49
48 47 46 45 44 43 42 41
40 39 38 37 36 35 34 33
32 31 30 29 28 27 26 25
24 23 22 21 20 19 18 17
16 15 14 13 12 11 10 9
8 7 6 5 4 3 2 1

A 'Move' is defined as a horizontal or vertical swap between adjacent cells on the board.

The puzzle is -- How many minimum 'Moves' are required to transform Board to Reverse-Board.

Much Love.
Rohit

1 Comments:

Blogger Termi said...

the answer to the above puzzle is :

for nxn matrix the number of moves are: 2n(n^2-1)/3.

-Termi

1:56 PM  

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