All the positive triangular numbers are written successively without commas or spaces resulting in this infinite string.

13610152128364555667891105120136153171..............

Determine the 2010^th digit in the above pattern.

DEFDBL A-Z
sought = 2010
FOR i = 1 TO 1000
  diff = diff + 1
  tr = tr + diff
  t$ = LTRIM$(STR$(tr))
  PRINT t$
  prevCt = ct
  ct = ct + LEN(t$)
  IF ct >= sought THEN
    d$ = MID$(t$, sought - prevCt, 1)
    PRINT diff; d$: END
  END IF
NEXT

finds as the last couple of lines of its output:

97903
 442 3

meaning that the sought digit is 3, being the last digit of the 442nd triangular number, 97903.

Posted by Charlie on 2010-07-20 13:50:02