Math Brain Teaser (1 Viewer)

[John Spencer]

Wouldja eat the moon if it was made of ribs?
I would.

 

[Bill Catherall]

"259?" - yes. I guess that was a little too easy.
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Bill

 

[Bill Catherall]

Here's another:
"A vine is climbing up and around a cylindrical tree trunk in a helical manner. The tree trunk has a height of 600 inches and a circumference of 40 inches.
If the vine covers a vertical distance of 75 inches in one complete twist around the tree trunk, what is the total length of the vine (assuming it has grown to the very top of the tree trunk)?" (No cheating, I found this online.)
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Bill

[Edited last by Bill Catherall on November 15, 2001 at 05:21 PM]

 

[Joseph Howard]

Mike got mine!! The answer was 66!
Solution follows:
Fraction of pole in the ground = ½ (or 3/6)
Fraction of pole covered by water = 1/3 (or 2/6)
Fraction of pole in the ground and covered by water = ½ + 1/3 = (3 + 2)/6 = 5/6
Fraction of pole out of water = 1 - 5/6 = 1/6
That means that the one-sixth of the pole (out of water) is 11 feet.
So, the total length of pole is 66 feet.

 

[Dheiner]

680?

 

[Bill Catherall]

John Dhein got it!
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Bill

 

[Seth Paxton]

Without looking at spoilers this seems pretty easy, maybe I missed something.
Spoiler:If on the 30th day the surface area doubled to cover the lake, then that means that before that the lilly was covering HALF the lake. Therefore if 2 lillies had been working independently at the same rate, they both would have HALF the lake covered by the 29th day.
2 lillies times half per lilly = lake covered on the 29th day

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Greetings from the Humungus! The Lord Humungus!
The Warrior of the Wasteland!
The Ayatollah of Rock and Rollah!

 

[Clinton McClure]

Bill - How many twists is the vine making around the tree trunk, or how far up the trunk from the ground (in inches) has the vine reached? Unless we know this, all guesses are purely speculation.
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My DVD Collection Casa del Clint

 

[Bill Catherall]

Clinton - I fixed the original question to add "(assuming it has grown to the very top of the tree trunk)." That should answer your question.
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Bill

 

[Clinton McClure]

Thanks. I hate making assumptions.

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My DVD Collection Casa del Clint

 

[Rives Elmore]

Should I even bother posting the Hotel Riddle??

 

[BrianW]

For those still working on Bill's Vine-Up-The-Tree-Trunk problem (despite knowing the answer), the easiest way to solve it (that I know of) is to Spoiler:employ the Pythagorean Theorem.
Here’s another one:
Two trains were involved in a head-on collision. Fortunately for all, the only casualty was a pesky fly that raced incessantly between the train engines as they were approaching one another. As soon as the fly reached the front of one train, it would immediately reverse itself and head for the front of the other train. (And, yes, the fly never slowed down, endured infinite acceleration while reversing direction, and all that.) The fronts of the trains and the fly all ended up in exactly the same spot when the collision occurred. Given that the trains were going a constant 30mph before the collision, and the fly was flying between them at a constant 50mph, where was the fly, in relation to the two trains, half an hour before the collision occurred?

 

[Micah Lloyd]

Rives,
Are you looking for the missing dollar?

 

[Bill Catherall]

Here what I get on the Train Crash problem: (Edit: need to change my answer and provide an explanation)
Spoiler:The fly is 12.066 miles from the closest train, moving towards the other train.
Ok...had to watch TV and come back to explain how I got it:
Spoiler:I started by assuming a start position for the trains and the fly. First I made a simple calculation that the trains would be 30 miles apart 30 minutes before the collision. Then assuming that the fly started at one train and headed to the other I noticed that for every "lap" the fly made (lap is the distance from one train to the other, half a round trip) the distance between the trains closed by 3/4. Or in other words, after every lap the new distance between trains was 1/4 the starting distance. And every lap the fly made was exactly .625 of the distance between the trains when the fly started the lap.
So I took that information and started from the collision and worked backwards. I had to make an assumption first though. I assumed that the fly was 1/4" long and that when the trains were 1/4" apart the fly would come to a "dead" stop. Any further motion of the trains would just result in squishing our little buddy. So starting with that and calculating backwards, the fly would have just finished a lap when the trains came 1/4" apart, so before the lap started the trains would have been 1" apart. (Yes, there's some error in this initial calculation because the fly's 1/4" length wasn't taken into account at the beginning of the lap. But since we're going to finish off in miles, I figure an error of even a yard won't matter, so what's a fraction of an inch.) Taking that further the next lap started with the trains 4" apart...and so on. This continues until the trains are 16.55 miles apart. The next backwards lap would result in the trains being farther apart than 30 miles, so now I just had to calculate the position of the fly at the 30 minute mark.
Adding up all the laps so far the fly has flown a total distance of about 13.79 miles. He would fly a total distance of 25 miles during his last 30 minutes of his life. So he has another 11.21 miles to make up. Since he's talking off from a train that is now about 8.27 miles from the center, at the 30 minute mark that will put him at about 2.93 miles from the center. Both trains are 15 miles from the center at this point leaving him approximately 12.066 miles from the closest train (I had my numbers wrong originally in my first answer had realized my mistake while typing up the explanation.) Now since we are working this backwards and he was flying towards the close train, if we run time forward again he's actually flying at the farther train and hasn't passed the center mark on this lap yet.
Whew!!
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Bill

[Edited last by Bill Catherall on November 16, 2001 at 12:45 AM]

 

[BrianW]

Nice going, Bill. With valid assumptions, you've come to a reasonable answer. However, I'd like to ask you a couple of questions:
Can you show that your answer is uniquely correct by placing the fly at a different starting point from your answer and demonstrating that the end result (the fly getting squashed at the same place, at the same time) will be different?
How many times did the fly reverse its direction in the last second of its life?

 

[Bill Catherall]

The fly gets squished in the middle no matter where he started 30 minutes before the collision. So I suppose my answer isn't unique. But here's what I found:
In my solution the fly reverses direction 7 times in the last second. The 7th reversal was just a turn with no movement. 3 of those reversals were done in the last hundredth of a second.
Starting the fly off from the exact center the fly will make 11.5 full laps (the .5 lap comes from starting in between the trains). At which time the trains will be .283 inches apart. Given that he is only a .250" fly he has .033" breathing room. But he gets squished before "finishing" the lap. (Technically his nose touched the train, but there is still a .071" gap between the trains if the center point of his body were to finish the lap.) He reversed direction 6 times in the last second. (3 times in the last hundredth of a second). He couldn't fit a seventh reversal (like my previous solution) because he was being compressed.
Starting the fly off from the front of one of the trains the fly makes 11 full laps. At the completion of the 11th lap the trains are separated by a gap of .453". If the center of the fly were to make a 12th lap then the trains would be .113" apart. So the fly gets squished before completing the 12th lap. He makes 6 reversals in the last second. (Again 3 in the last hundredth of a second.)
So although the starting point has no bearing on his final demise, with my solution he can fit in one additional turn before his brain meets his butt.
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Bill

 

[Dheiner]

Nevermind
[Edited last by John Dhein on November 16, 2001 at 02:06 PM]