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

I copied the layout into MS Excel and reformated the width of the cells.  I copied that cell style across the page for a reason distance (4 or 5 games).

I copied the initial layout to a lateral position and exchanged 4 & 5.
I copied that move and pasted laterally. 
I then diagonally exchanged 4 & 7.

In due course copied to the start of a 'new line'.

I sense that, if I continue to do this properly, by the time I reach halfway(and how will I recognise that?), the moves that I have  further to make could be considered as being a rotated, but reverse mirror of those moves.

The problem I am finding is to remember to swap two cells before copy and paste.

Course I could take a deck of cards, extract 1-9 and either J or 10  becomes 0.  But then you have to tally and record moves.

This is a challenge for Penny and Charlie!!

Posted by brianjn on 2005-07-06 11:20:25