Math/Logic Riddles

[gir]

I have two separate riddles I need solved. The first two may or may not be linked. Please and thank you!

5,6,9,10,4,?,5
501,10,999,4,1,?,11,500

Here are the other ones:

half of X = V; half of IX = ?; half of XI = ?

[ChrisV]

[ QUOTE ]
501,10,999,4,1,?,11,500

[/ QUOTE ]

The answer to this is 1001. If you convert all those numbers into roman numerals, it looks like this:

DI X IM IV I ? XI D

Replacing ? with MI completes the palindromic string:

DIXIMIVIMIXID

MI = 1001, so the answer is 1001.

I've been trying to do something similar with the first one, I think it might also be something along those lines, but I can't seem to make it work.

The last one is kind of a weird problem that seems like it should admit of several solutions. One "solution" that comes to mind is to chop the number through the middle horizontally, as is done for X to get V. This would yield half of IX = IV and half of XI = VI.

[gir]

You have a beautiful avatar. I figured out that the answer to the top one is 1. And that solves my riddle! I don't need the other one anymore! Thank you so much! =D

[ChrisV]

I neeeed tacos! I need them or I will explode! That happens to me sometimes /images/graemlins/frown.gif

btw, why is the answer to #1 1?

[gir]

I have no clue, I just kept single digits until it worked. That's how I solve riddles...I just push buttons and put in random answers until I'm eventually right.

"Gir, why is there bacon in the soap?"

[ChrisV]

I MADE IT MAHSELF!

[Philo]

As with any of these "sequence" type puzzles, there is no unique solution here. There are an indefinite number of possible answers, all of which would fit some pattern or algorithm that explains the sequence. Some of these patterns are just more apparent or familiar to us than others (like a prime number sequence, for example).