A train crosses a labeled bridge
Python 2, 110 105 104 103 100 97 96 bytes


Saved five bytes thanks to Mr. Xcoder; removed unnecessary assignment, moved negation into available whitespace.
Saved a byte thanks to Mr. Xcoder; golfed [~-x:x+~-t] to [~-x:][:t].
Saved a byte; golfed ...range(1,-~b)))[:b] to ...range(b)))[1:-~b].
Saved three bytes; golfed [1:-~b][~-x:] to [:-~b][x:].
Saved three bytes; golfed [:-~b][x:] to [x:-~b].
Saved a byte thanks to Lynn; golfing the while loop to an exec statement.




b,t,x=input();S=x;exec"x+=sum(set(map(int,''.join(map(str,range(b)))[x:-~b][:t])));"*b;print-S+x


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