
4
Was going to whip this out, then realized that I needed more preparation. :P
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Welp, other people have gotten into trying to beat FOOT, so I figured I might as well try my hand at it.
With a decided lack of originality, I've decided to name my system FOFT (First Order Functional Theory). As the name suggests, the fundamental new objects are functionals on ordinals. Functionals are defined as follows:
Let \(F_\alpha\) denote the set of \(\alpha\)functionals.
A 0functional is just an ordinal.
A \(n+1\)functional is a function from \(F_n\) to \(F_n\). Equivalently, it is a function from \(\prod_{i=1}^n F_i\) to \(F_0\). (You can see this by repeatedly applying the definition of \(F_i\) in the range  for example, \(f: F_3 \mapsto F_3 \implies f: F_3 \mapsto (F_2 \mapsto F_2) \implies f: F_3 \mapsto (F_2 \mapsto (F_1 \mapâ€¦
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Okay, the Second Googological Olympiad has officially ended. Four people sent in solutions, and two sent in solutions to all six problems. The winner is Wojowu, who scored a stellar 47 out of 50 points. On April 15, a person named January FirstofMay sent in solutions; while technically his scores should not count, I don't see a problem with adding his scores to the list.
Results of the Second OlympiadNameP 1P 2P 3P 4P 5BonusTotalWojowu55101010747Wythagoras55596131Cloudy17655 10January FirstofMay55 10cookiefonster5 5
Thanks to everyone who participated! I had a lot of fun writing and overseeing the contest.Solution to Problem #1:
The answer is \(\prod_{i=0}^{n1} 10[3]i\), where we take \(10[3]0\) to be \(10\). In fact \(10[3]nâ€¦
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Welcome to the Second International Googological Olympiad! Rules are as follows:
 There are 5 questions and a bonus question, worth a total of 50 points.
 Contest ends at 23:59 PST on April 12, 2015.
 Solutions are to be mailed to my email address. It is an account at hotmail.com, and the user name is my name (Royce Peng).
 If anyone needs clarification, please bring it up in the comments. However, please do not spoil any question by giving away the answer or saying something that gives insight into solving the problem. If you cannot do so, or are not sure whether your comment will be a spoiler for the problem, please email me with your question instead.
 Please do not discuss the problems with each other before the due date.
 I will try to respond â€¦

So, I'm thinking of starting the next Googological Olympiad shortly, and I was wondering whether people had any comments regarding how it should be administered.
How long should I run it for?
Should I give immediate feedback, or wait until the competition is over?
If I give feedback, should I allow resubmission of solutions?
I was thinking of varying the number of points each question is worth. Is this a good or bad idea?
Thanks in advance for any comments!
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