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Wythagoras 17 August 2016
1

## My BF programs

I found the following program:

+>+>...+>+> ++...++ [->[>]+>+>+>+[->[>]+>+>+>+[->[>]+>+>+>+[->[>]+>+>+>+>+[->[>]+>+>+>+>+[->[>]+>+>+>+>+>+[->[>]+>+>+>+>+>+[->[>]
Wythagoras 24 July 2016
5

## The nineteenth Busy Beaver number is greater than Graham's Number!

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 $\Sigma(18) > f_{\omega+1}(7\cdot10^{57}) > G.$

• 1 Machines that need input
• 1.1 10 state, 2 color machine with Ackermannian growth
• 1.2 14 state, 2 color machine with expandal growth
• 1.3 14 state, 2 color machine with expandal growth, variant
• 1.4 14 state, 2 color machine with expandal growth, second variant
• 1.5 17 state, 2 color machine with multiexpandal ($$f_{\omega+2}(n)$$) growth
• 1.6 20 state, 2 color machine with powerexpandal ($$f_{\omega+3}(n)$$) growth
• 2 Machines that don't need input
• 2.1 5 state, 2 color machine that outputs 165 consecutive ones
• 2.2 15 …

Wythagoras 23 February 2015
8

## Results of the First International Googological Olympiad

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.

• 1 Results
• 2 Acknowledgements
• 3 Problems
• 4 Solution to problem 1
• 5 Remarks to problem 1
• 6 Solution to problem 2
• 7 Solution to problem 3
• 8 Solution to problem 4
• 9 Remarks to problem 4

Congratulations to all contestants. Fish is the winner of the contest.

These scores are 0.0 because I ha…

Wythagoras 25 January 2015
12

## Problems for the First International Googological Olympiad

• 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.
Wythagoras 25 January 2015
3