Let x be the initial number of toy soldiers that Matthew had.
Matthew gave 1/2*x toy soldiers to Nigel, so Nigel had x/2 soldiers.
Nigel gave 3/7*(x/2) = 3/14*x toy soldiers to Oscar, so Oscar had (1-3/14)*x = 11/14*x toy soldiers.
Oscar gave 1/5*(11/14*x) = 11/70*x toy soldiers to Mathew, so Mathew had x-(11/70*x) = 59/70*x toy soldiers in the end.
Each person had 59/70*x = x/3 toy soldiers.
Thus, 59/70*x = x/3.
Multiplying both sides by 3*70 = 210, we get 177x = 70x.
Therefore, Matthew initially had 177-70 = <<177-70=107>>107 more toy soldiers than Oscar. Answer: \boxed{107}.
Matthew, Nigel and Oscar had 84 toy soldiers altogether. Matthew gave 1/2 of his toy soldiers to Nigel. Then Nigel gave 3/7 of his soldiers to Oscar.
Finally, Oscar gave 1/5 of his soldiers to Mathew. In the end, each person had the same number of toy soldiers. How many more soldiers did Matthew have than Oscar initially?
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