the king had 3 sons.
each of them had 2 sons. (that makes 3 out of 100 offsprings, who had 2 offsprings).
each of the 6 grandsons had 2 sons, which makes 12 more sons (3+6 / 100).
the 12 sons of this generation all had 2 sons, which makes 24 more kids. (3+6+12 / 100).
each of the 24 had 2 sons, and another 48 offspring (and 3+6+12+24 out of 100 allowed offspring have had 2 sons).
the 48 sons have all 2 sons. 3+6+12+24+48=93, so 7 of the 96 sons of this generation may have 2 sons.
this makes 14 more sons, and no more can be born.
adding all together, we have 3+6+12+24+48+96+14=203.
each of them had 2 sons. (that makes 3 out of 100 offsprings, who had 2 offsprings).
each of the 6 grandsons had 2 sons, which makes 12 more sons (3+6 / 100).
the 12 sons of this generation all had 2 sons, which makes 24 more kids. (3+6+12 / 100).
each of the 24 had 2 sons, and another 48 offspring (and 3+6+12+24 out of 100 allowed offspring have had 2 sons).
the 48 sons have all 2 sons. 3+6+12+24+48=93, so 7 of the 96 sons of this generation may have 2 sons.
this makes 14 more sons, and no more can be born.
adding all together, we have 3+6+12+24+48+96+14=203.