Question 300773
EVELYN wrote her name 200 times in a row without a space between them. What letter is written in the 100th space? in the 196th space?
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If she wrote it only three times

E  V  E  L  Y  N  E  V  E  L  Y  N  E  V  E  L  Y  N
1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 
to find out what was in the 17th space we divide the
number of letters in EVELYN, which is 6, into 17

   2
6)17
  12
   5

The quotient 2 tells us how many times the name has been
completed before the 17th letter, and the remainder tells
us that how far into the name the 17th letter is into the
next or 3rd writing of the name.  So the 17th letter is 
the same as the 5th letter or Y.

It's the same principle no matter how large the number is,

   16
6)100
   6
   40
   36
    4

So the 100th letter is the same as the 4th, or L

   32
6)196
  18
   16
   12
    4

So the 196th letter is the same as the 4th, or L.

Edwin</pre>