When in doubt, put it to the t-test.
You can flip the top row 180 degrees on the horizontal axis, and the next number that fits would be 111.This would suggest that the second row flips on the vertical axis somehow, and 2, 5 sorta turn into each other that way, so I'll guess 33, but I don't think I'm quite getting that one.
Sorry, that should be a 180-degree twist.
I can't disagree on sequence 1, but I can't say that I'm sure it's right.But the rule AVI gives says that the next value should be 111.On the second sequence, I think the next value is 55. Whatever pattern draws 1,2,5,8 together looks to continue as 11,22,55,88. But that's mostly a guess.
AVI is right for the first one, wrong on the second.SJ got the second one right, but missed the reason...I'm curious if anyone can figure out what the correct reason is. Also, another reader alerted me to the fact that there's actually a name for the numbers in the first part: strobogrammatic numbers. I give extra credit for that.
The first row of numbers reflects on the horizontal access if handwritten, the second row reflects on the horizontal access if they are typed in to a (basic digital) calculator.