Monstrous Mishmash
I've just worked through an old ForSmarts Puzzle Book, September '06, issue 1. The Chess Battleships are a pleasing variant.
I caught a bit of "Tron" on G4 a while back, and I've been trying to model that game with the disappearing ring platforms. Players alternate serving an energy ball with a jai alai cesta, bouncing it off the ceiling to hit the other player's circular territory. If the other player fails to catch the ball and it hits the platform, one of several ring-shaped areas disappears from play and the original player serves again. Whoever falls off their platform loses.
My idea was to determine how likely it is that a player will need to cross a certain ring, given its inner and outer radii, so that its elimination necessitates an opponent to jump/sidewind/time his steps. It seems obvious that eliminating a ring of medium radius causes more difficulty for a player than eliminating the outermost ring or the center, so I'd like to find which ring occludes the most straight line segments inside a circle. Unfortunately, the term for a line starting outside the ring is a deathly complicated integral.
Setting that aside for a while, I noticed this thread looking for the smallest pentagonal number with the letters "PENTAGONAL" in its name from left to right. The answer that's there now is wrong for a couple of reasons. It's not pentagonal, or even prime (the digits add up to 18), so "ken" couldn't have been trying for that. Further, putting "And" in the name, while common, is nonstandard, frowned upon, and cheating since the example didn't have that word. Fortunately, not only did I find the correct answer, but it turned out to be much smaller, since I used 17 instead of 70 for ENT.
And now, here is the 816,496,588,003rd pentagonal number: 1,000,000,017,330,402,836,998,012 (one sePtillion, sevENTeen quAdrillion, three hundred thirty trillion, four hundred two billion, eiGht hundred thirty-six milliON, nine hundred ninety-eight thousAnd, tweLve). Not much to look at, I know, but at least it's out of my system.
By the way, for Halloween? I finished my costume in time. However, I decided to vote early on that day, so not many people saw the costume. I did have pictures taken, though, so try to guess who/what I was before I put them up. (Hint: it's ironic that I don't have a puzzle for this, and his name is Billy.)
I caught a bit of "Tron" on G4 a while back, and I've been trying to model that game with the disappearing ring platforms. Players alternate serving an energy ball with a jai alai cesta, bouncing it off the ceiling to hit the other player's circular territory. If the other player fails to catch the ball and it hits the platform, one of several ring-shaped areas disappears from play and the original player serves again. Whoever falls off their platform loses.
My idea was to determine how likely it is that a player will need to cross a certain ring, given its inner and outer radii, so that its elimination necessitates an opponent to jump/sidewind/time his steps. It seems obvious that eliminating a ring of medium radius causes more difficulty for a player than eliminating the outermost ring or the center, so I'd like to find which ring occludes the most straight line segments inside a circle. Unfortunately, the term for a line starting outside the ring is a deathly complicated integral.
Setting that aside for a while, I noticed this thread looking for the smallest pentagonal number with the letters "PENTAGONAL" in its name from left to right. The answer that's there now is wrong for a couple of reasons. It's not pentagonal, or even prime (the digits add up to 18), so "ken" couldn't have been trying for that. Further, putting "And" in the name, while common, is nonstandard, frowned upon, and cheating since the example didn't have that word. Fortunately, not only did I find the correct answer, but it turned out to be much smaller, since I used 17 instead of 70 for ENT.
And now, here is the 816,496,588,003rd pentagonal number: 1,000,000,017,330,402,836,998,012 (one sePtillion, sevENTeen quAdrillion, three hundred thirty trillion, four hundred two billion, eiGht hundred thirty-six milliON, nine hundred ninety-eight thousAnd, tweLve). Not much to look at, I know, but at least it's out of my system.
By the way, for Halloween? I finished my costume in time. However, I decided to vote early on that day, so not many people saw the costume. I did have pictures taken, though, so try to guess who/what I was before I put them up. (Hint: it's ironic that I don't have a puzzle for this, and his name is Billy.)