I think the Uud's were on Doctor Who (maybe spelled Ood).
Ed, I find this unusual. Is there a reason for this sequence?
Here is a version with a single graphic (so it is easier to annotate with arrows):
texts = MapIndexed[Text,
Table[7 n (n - 1)/2 + If[OddQ[n], {0, 4, 5}, {5, 4, 0}], {n, 1,
10}], {2}];
FindNextNumbers[Text[n_, {x_, y_}], texts_, dx_] :=
Select[texts, Abs[#[[1]] - n] == dx &]
list = Module[{dx = 5},
Most[NestWhileList[
With[{choices = FindNextNumbers[#, Flatten[texts], ++dx]},
Switch[Length[choices], 0, None,
1, choices[[1]],
_, Print["error ",Length[choices]]; None]] &,
texts[[1, 3]], # =!= None &]][[All, 2]]];
Graphics[{texts, {Red, Arrow /@ Partition[list, 2, 1]}}]
Of course, I wonder about other chess move sequences.