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I found the following program:
+>+>...+>+> ++...++ [>[>]+>+>+>+[>[>]+>+>+>+[>[>]+>+>+>+[>[>]+>+>+>+>+[>[>]+>+>+>+>+[>[>]+>+>+>+>+>+[>[>]+>+>+>+>+>+[>[>] Read more > 
I found some improvements to Deedlit's original Ackermannian growth and expandal Turing Machines.
Using this, I can prove that \(\Sigma(19) > f_{\omega+1}(163) > G\).
Note: I found a machine that proves \[\Sigma(18) > f_{\omega+1}(7\cdot10^{57}) > G.\]
Somehow states 3, 4 and 5 are completely obsolete in the original machine.
In fact, removing them even increases the first string by three ones instead of two.
0 1 1 l 0 0 _ 1 r 2 2 1 1 r 2 2 _ _ r 6 6 _ _ l halt 6 1 1 r 7 7 _ _ r 6 7 1 1 l 8 8 1 _ l 9 9 _ _ l 10 9 1 1 r 11 10 1 1 l 9 10 _ 1 r 0 11 1 _ r 12 11 _ _ l 13 12 _ 1 r 11 12 1 1 l 13 13 1 1 l 13 13 _ 1 l 10
You can simulate the machine on Anthony Morphett's site.
This also works in the expandal growth machine, as that is just an extension oâ€¦
Read more > 
The First International Googological Olympiad has ended. Here will follow the results, remarks and solutions. In the First International Googological Olympiad (FIGO for short) have participated four contestants, of which three have sent all problems to me. I consider the olympiad as a succes, given the fact that all contestants responded very positive. I've learned a lot of this olympiad as well (see the acknowledgements section), and I've enjoyed organizing it.
Congratulations to all contestants. Fish is the winner of the contest.
Contestant Attempt P1 P2 P3 P4 Penalty Total
Fish #2 7.0 7.0 7.0 7.0 1.0 27.0
#1 7.0 7.0 7.0 3.0 0.0
LittlePeng9
7.0 7.0 4.0 7.0 0.0 25.0
Deedlit11 #2 7.0 7.0 4.0 7.0 2.0 23.0
#1 7.0 3.0 4.0 7.0 0.0
Vel!
7.0 0.0* 0.â€¦
Read more > 
 You can send your solutions to my mailadress.
 If you don't know my mailadress, you can leave a message on my talk page with your mailadress, so that I can mail you. If you don't want that, make an appointment on my talk page, and you can tell it in chat.
 Everyone can participate.
 You can participate anonymously, but at least give a pseudonym.
 If you have questions about the problems you can ask in comment.
 Please do not discuss the problems before the due date.
 You need to give proofs, only answers aren't enough.
 There are four problems worth seven points each.
 The maximal score is seven points. The minimal score is zero points.
 Due date: February 22, 2015, 23:59 UTC.
 If you've sent your solutions, you can leave a comment here. I'll look to them asâ€¦
 You can send your solutions to my mailadress.

I was thinking about organizing a Googological Olympiad. I have already made a problem set. If there are at least 3 candidates, I will organize the olympiad, otherwise, I'll just post the problems. So:
Also, if you want to practice:
 User blog:Wythagoras/Googological problems I.
 User blog:Wythagoras/Googological problems II.