A* Admissible Heuristic for die rolling on grid

Question

I need some help finding a good heuristic for the following problem:

You are given an R-by-C

Answer 1

Well, I'll add my comment here, since it is more optimal than the current highest-voted answer by @larsmans - but, I am convinced there must be something better (hence the bounty).

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If I multiply the heuristic with a constant, it's no longer admissible

The best I can come up with is (manhattenDistance/3)*6 + (manhattenDistance%3), where / is integer division and % is mod. This works because in any 3 moves with no back-tracking, all three digits will be unique, so the lowest sum we could have is 1+2+3 = 6 (The %3 simply adds any extra, non-multiple-of-three moves).

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[Edit] As @GrantS pointed out in the comments above, my heuristic can be improved very slightly by adding an additional 1 when manhattenDistance%3 == 2. This is easy to do without a conditional: (manhattenDistance/3)*6 + (manhattenDistance%3)*3/2