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.
Monday, December 31, 2007
Sunday, December 09, 2007
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.
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 !!!"
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 !
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 ?
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