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 !!!"

---

How many troops would be sacrificed ?

The Cursed Pirate Gold

Once, there were 7 pirates. The pirates had just robbed a small fishing boat and were now splitting the loot.

The loot was a small chest of less than 500 gold coins. The 7 pirates decided to split the loot evenly between themselves, as they were petty and did not want any one member to get more loot.

After a while, the gold coins were split into 7 stacks. However, the 7th stack had 1 coin less than the others. An argument broke out over who was to receive this 7th stack, and during the heated debate, one pirate was "accidentally" killed.

While the loss of manpower was regretable, the pirates consoled themselves with their now larger shares of the loot. Again, they pooled the coins and split it evenly among themselves. After some splitting, the coins were split into 6 stacks. Alas, the 6th stack was again 1 coin short!

A new scuffle broke out and another pirate was killed. The remaining 5 pirates split the coins into 5 stacks. Cursedly, they were 1 coin short again of having even stacks! One of the pirates, shocked at this unnatural occurence, shouted "A Ghost ! It be the work of ghosts !", then flipped over and died.

While the remaining 4 pirates were unnerved, greed was a stronger motivator. They split the gold into 4 stacks, but again, they were short by 1 coin !!! The burliest member of the band of brigands, a person of vulgar courage, slammed his fist on the table and shouted "I fear no work of demons ! Give me my gold !". He was swiftly killed by a falling lamp which was dislodged by his slamming action.

3 pirates were left, and they were clearly spooked. Yet, they divided the loot into 3 portions. One member, on seeing that one stack was again short of 1 coin, feared for his life and ran, leaving his share untouched !

The 2 remaining pirates decided to make the best of things and split the loot again, this time evenly among themselves. But the stacks were again uneven!

By now, the 2 pirates were spooked and decided to flee for their lives !

---

How many gold coins were there originally ?

Epilogue : The world of the purple sky

And none were the wiser, that that which seemed the same, was not.

The unknown truth was that the professor was still on the Earth. He was not dead, nor was he missing. He did not hide, nor was he hidden. The simple truth was that he was still where he had started his grand experiment.

It was not strange that nobody could find him, because none ever knew what his grand experiment really was.

The purple hue was only to hide the missing stars.

And none were the wiser, that that which they thought was the earth, was not.

---

Read the first part of the story here.

The world of the purple sky

The professor went missing three weeks ago. Prior to his disappearance, he was conducting yet another of his secretive experiments, which he described as being his “most amazing discovery”. We were all skeptical.

On the night he disappeared, a purple haze enveloped the sky, stretching beyond the horizon. It drew us to his home, but we could find nothing. Even his house had disappeared.

From that day on, the sky was draped in that cursed purple hue. We never managed to find the professor. He had vanished from the face of the earth, lost to an unknown space and time.

What's In a Name ?

Recently, some bloggers put up simple "Free Burma !" posts on their blogs. Then, yesterday, I saw someone on MSN with the nick, "Free Myanmar !".

Two words, refering ostensibly to the same object, and yet having absolutely different connotations.

Not too long ago, I was puzzled by the absolute refusal of certain global entities in using the name "Myanmar". After all, what's in a name, or so I thought. Then came the recent crisis in Myanmar/Burma, which highlighted the otherwise subtle differences in the words.

The fact that the choice of a noun actually indicates the person's political position is extremely interesting. However, in retrospect, this is not new - "Pro-choice", "Pro-life", are both terms which refer to the same thing, but signify different stances towards abortion. Many other examples exist.

Thus, I wonder - Is there a neutral word which can be used to refer to Myanmar/Burma ? With only two words to chose from and with each word implying the supporting of a particular faction, in naming that country, one would forcibly dragged into taking a side. Interesting, and troublesome, for any self-purported neutral observer.

Free Temasek, anyone ? Or, perhaps, free Malaya.

FOOD WAR

A war was waged, for the most mundane of reasons, in the most unlikely of places - a lecture theatre. The instigator of the war, motivated only by a need to satiate his boredom, thus began the FOOD WAR.

The 16 contestants, called from the recesses of the minds of the mad, fought for votes from the panel of bored judges.

Eventually, SUSHI won.



PS : Note contestant number 5.

Unfair Coin and Die Challenge

[Challenge #1]

Imagine that you have a biased two-sided coin. However, while you know that the coin is biased, you are unsure as to how the coin is biased; that is, you do not know the probability of getting a head or tail.

The first challenge is to use the coin to make a binary decision that has a 50% probabilty. In other words, find a way to make a fair decision.


[Challenge #2]

Imagine that you have a biased 6 six-sided die. As before, you have no idea how the die is biased.

The second challenge is to think of a method to somehow transform (via mathematical, non-physical-manipulation methods) the die into a fair die.

[Hints]
It may be neccessary to flip the coin more than once. Same goes for the die.

[Super Hints]
"May be" ==> "is".