The numeric keyboards of a telephone (left) and a pocket calculator (right) differ in the arrangement of the keys.

123   789
456   456
789   123
  0      0

What is the least number of moves necessary to transfer the keys of the first arrangement into the other arrangement?
One move consists of switching the position of two neighbouring keys (Horizontal, vertical or diagonal) of which the sum is 9, 10 or 11.
Example: In the starting position you can switch 6 and 3, 5 and 6, 4 and 5, 7 and 4, 0 and 9

In the first column, swap 1 for 4, 1 for 7 and 7 for 4 and we have made 3 moves.  Following the same procedure for Cols 2 & 3 and we have 9 in total.

However, the sum rule has not been considered, although it did happen, 4 times in all during this process.

Posted by brianjn on 2005-07-06 07:02:26