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I found a game with a very unique and interesting gameplay, one which was so fresh that I had never seen before. I was so impressed by the game that I had to introduce it here.
I can't reveal much about the game without spoiling it. All that I can say is that the game requires you to "Cooperate by oneself ?!".

By the way, my (unimpressive) high score is 139. It is probably easy to beat this, but I don't want to click madly again.

Hope everyone enjoys this short game.

Test your Induction

The following sequence of three characters obeys a certain secret rule.

2, 4, 6

Your task is to infer the secret rule. To help you to discover the secret rule, you can produce any number of three character sequences for testing. I will then reply whether the produced sequence(s) obey the secret rule. (Pls try to propose sequences only in the tagboard; I will update the tested sequences in this post.)

As you can propose any number of character sequences for testing, you should only attempt to report the secret rule when you are absolutely sure that you have the correct rule in mind. To keep the game suspenseful, post rules only in the comments.

Why are the Month Lengths Irregular?

I consider the lengths of the months to be irregular. I came to this conclusion after I asked myself the question, "How would I distribute the 365 day calendar into 12 months ?".

My (intuitive) solution was to divide 365 by 12. This leaves 30 days per month, with 5 days left over. A reasonable split would be 7 months of 30 days, and 5 months of 31 days. Regarding the ordering of the months, I considered 2 ways. The first would be to place the 5 odd months at an end of the calendar (either the front or the back). However, after some consideration, I felt that this method, while being easy to remember, seemed unsymmetric, and might leave the halves of the calender unbalanced. My second idea was to alternate the long and short months. The last 3 months would be short.

The resulting calender would be : 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 30, 30.

Evidently, this is quite different from the current form of the calendar. The current calendar has 7 months with 31 days, 5 months with 30 days, and 1 month with 29 days. This is clearly an arbitary arrangement of days. This leads me to the conclusion that the calender was not created and imposed at a single moment in history by a single planner or authority, but rather the result of a series of incremental changes.

Here's how I hypothesise the calendar came about (based on pure speculation alone):

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Original creator : Let's make a 365 day calendar with 12 months ! The calendar should be symmetric around the center.
Result : 31, 30, 31, 30, 31, 30, 30, 31, 30, 31, 30, 31

Problems : 366 day calendar.
Solution : Borrow 1 day from some random month.
Result : 31, 29, 31, 30, 31, 30, 30, 31, 30, 31, 30, 31

After some time : Hey let's make this month longer ! For no reason !
Result : 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31

Problems : 366 days again ! You clown !
Solution : Pick on the loser month with 29 days. Easier to recall which month is odd.
Result : Existing calendar.

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Of course, the previous speculation was utter nonsense. However, I do believe that the present calendar was slowly morphed from a predecessor calendar slowly. The gradual changes were implemented such that the newer calendars would be minimally different from the earlier calendars. In other words, if they added a day to another month, and needed to remove a day from an existing month, the best candiate would be a month which was already an oddity.

Perhaps that is why February is such a 'loser' month. It's at least 2 whole days shorter than everyone else, and even at it's best it's still shorter by 1 day. It must have been the victim of multiple 'shortenings' !

Simplicity

Occam's razor, expressed as "Of two equivalent theories or explanations, all other things being equal, the simpler one is to be preferred", emphasizes simplicity over complexity. Yet, what is simplicity ? I suspect that there can be no answer to the question (or, rather, no simple answer to the question).

Simplicity is a concept that is dependent on the viewer, and different viewers would have differing ideas of the simple. Unfortunately, due to the mental and psychological similarities between most humans, this fact is not immediately obvious. Given two differing items, most people would agree on which is simpler. For example, most people would find the equation "2 X 2 = 4" as a simpler variant of the phrase "Integral of 2 over the bounds of 0 to 2". And yet, for a hypothetical person who was taught calculus before arithmetic, the reverse would be true. Hence, simplicity is really dependent on the viewer.

Queer Altering of Behavior

I find it interesting that when people visit foreign lands, their behavior is often different from their usual state. This effect is particularly evident in tourists.

Consider a person A, who is usually unadventurous in his choice of food. And yet, upon arrival at the foreign land, A decides to try each and every kind of strange food he chances upon. Queer.

Or that A decides to climb a famous mountain, and yet, A has never even mounted the hill back in his native land. Odder and odder.

Fortunately, I am rational and consistent. My behavior is similar to my original state, with the only difference being that I have more cash to spend, and that spending all the cash is acceptable.

This is the last post of the year. I shall now take some photos of the fireworks, although I consider that to be irrational and inconsistent with my initial state.

This irrationality must be corrected.

Kill the Penguins !

Penguins led by the evil Guin Nep have invaded an iceberg ! There are so many penguins on the iceberg that every inch of the iceberg is covered with penguins.

You have to stop the infestation of penguins! You have 5 rockets, which can be used to bombard the iceberg. The rockets are all identical, and can hit any area of the iceberg. Each rocket will explode and kill all penguins within a radius Z of its landing spot. The yield of the rockets can be adjusted, hence, Z can be set to any value you desire. However, all the rockets must be set to the same yield, otherwise the launching platform will malfunction.

Your task is to choose 5 spots to target the five rockets at. Also, you must choose the minimum yield needed to kill all the penguins. In other words, choose 5 spots and the smallest Z such that the each spot of the iceberg is covered.

The final piece of information needed before you can save the iceberg from the penguins is that the iceberg happens to be in the shape of a perfect circle of radius R.

Alien Invaders

The great conqueror of worlds, Cyotr IV, was planning for the invasion of yet another planet. His advisor, the evil Guin Nep, stood beside him.

The great conqueror asked, "How many troops do I have available for this invasion ?"

Guin Nep checked some statistics, then replied, "Oh great one, you have a hundred thousand galaxy clusters under your control. In each galaxy cluster, there are a billion billion galaxies. In each galaxy, there are a billion billion stars clusters. In each star cluster, there are a billion billion stars. For each star, there are a billion billion divisions stationed there.

Finally, there are a billion troops per division. These figures work out to 10^86 troops. The figures are exact."

The conqueror paused for a moment, contemplating the great vastness of his forces.

"Split ALL my forces into 13 even fleets ! Prepare for the invasion of the universe !!!"

"13 even fleets, sir ? We won't be able to split the troops evenly; there'll be some troops left over. I would advise dividing the forces into 10 fl..."

"DIVIDE THE TROOPS INTO 13 EVEN FLEETS ! SACRIFICE THE LEFTOVER TROOPS !!!"

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How many troops would be sacrificed ?