Sunday, December 09, 2007

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..."


How many troops would be sacrificed ?


lightsaber8884 said...

One unlucky trooper.

The Negative Man said...

Eh wrong. Any reasoning ?

lightsaber8884 said...

Sorry my bad: It should be 100 troopers. 86 = 6(13) + 8.
By Fermat's Little Theorem,
10^86 = (10^(13))^6 * 10^8 = 10^6 * 10^8 (mod13) = 10^14 = 10^13 * 10 = 10*10 (mod13) = 100.
Made a careless mistake.

The Negative Man said...

Yeah, your answer is correct.

Although, I observe that you like to use powerful theorems to solve problems. Like using a lightsaber to cut meat.

lightsaber8884 said...

Hmm... actually 100 still isn't the right answer... I can still divide the 100 by 13, which gives me a final remainder of 9.

The Negative Man said...

Yah. I assumed that was what you meant.