[Prof. Templeton]

1.) A utility company had to run electrical poles 10 miles between town A and town B over a hill. They discovered that the railroad company was also running a track from town A to town B but was making a level cut through the hill that would make their track 9 miles long. The utility company decided to run their poles alongside the level track, through the hill, instead over it. The utility poles need to be 99 feet apart. How many poles did the utility company save be running them alongside the track and not over the hill?

2.) There is a particular village in Madagascar that lies in a very low valley and yet at noon the sun is over 3,000 miles closer to the inhabitants of this village then when it either rises or sets. What part of the country must the village be in?

3.) If the end of the world were to occur on the first day of a new century sometime in the next 2000 years, what are the chances that it will happen on a Sunday?

4.) Leading up to a temple in Nepal there is a stairway with eight steps, not counting the landings, and the monks who worship there have a curious ritual. They start from the bottom and step onto the top landing twice (having to finish there) and return to the bottom landing once being careful to step on each step the same number of times. They always do this in the least number of steps. How many steps do the monks take?

[bonanova]

53 poles

Floor[1+533.33] - Floor[1+480]

[Prof. Templeton]

53 poles

Floor[1+533.33] - Floor[1+480]

I think it's less.

[Guest]

1.) A utility company had to run electrical poles 10 miles between town A and town B over a hill. They discovered that the railroad company was also running a track from town A to town B but was making a level cut through the hill that would make their track 9 miles long. The utility company decided to run their poles alongside the level track, through the hill, instead over it. The utility poles need to be 99 feet apart. How many poles did the utility company save be running them alongside the track and not over the hill?

2.) There is a particular village in Madagascar that lies in a very low valley and yet at noon the sun is over 3,000 miles closer to the inhabitants of this village then when it either rises or sets. What part of the country must the village be in?

3.) If the end of the world were to occur on the first day of a new century sometime in the next 2000 years, what are the chances that it will happen on a Sunday?

4.) Leading up to a temple in Nepal there is a stairway with eight steps, not counting the landings, and the monks who worship there have a curious ritual. They start from the bottom and step onto the top landing twice (having to finish there) and return to the bottom landing once being careful to step on each step the same numbe

20 steps

r of times. They always do this in the least number of steps. How many steps do the monks take?

Edited March 20, 2009 by Tailwind62

[bonanova]

The difference for a city at the equator would be the radius of the earth 3963 miles give or take.

Anywhere else the difference would be multiplied by Cos [latitude].

cos^-1 {3000/3936} appears to be about 41^o.

So the difference would be 3000 miles or greater between 41 N and 41 S latitude.

Madagascar lies totally within that range.

If we're looking for the closest to 3000 miles, we'd have to go with the southern tip of the island.

[Prof. Templeton]

20 steps

Close.

[Prof. Templeton]

The difference for a city at the equator would be the radius of the earth 3963 miles give or take.

Anywhere else the difference would be multiplied by Cos [latitude].

cos^-1 {3000/3936} appears to be about 41^o.

So the difference would be 3000 miles or greater between 41 N and 41 S latitude.

Madagascar lies totally within that range.

If we're looking for the closest to 3000 miles, we'd have to go with the southern tip of the island.

For over-thinking.

I would have accepted

Spoiler for the answer:

anywhere.

[Guest]

I can get to 12 if they can skip steps

1 for each step 2 steps on top 2 on bottom

Close.

[Prof. Templeton]

I can get to 12 if they can skip steps

1 for each step 2 steps on top 2 on bottom

No skipping, but I think you must have the right idea. Can you number your steps (like maybe B,1,2,3,4,5,6,7,8,T) and produce your sequence?

[Guest]

I think it's less.

Don't you mean more?

0.15

[Guest]

No skipping, but I think you must have the right idea. Can you number your steps (like maybe B,1,2,3,4,5,6,7,8,T) and produce your sequence?

12345678t87654321b12345678t = 27

[Guest]

12345678t87654321b12345678t = 27

19 is the minimum.

[Guest]

19

[Prof. Templeton]

0.15

Don't you mean more?

Nope, I mean less for No.1 and also No.3

19 is the minimum.

19

That's it!

[Guest]

Nope, I mean less for [...] No.3

Well, I had a 6/7 chance of being right. The only other possible answer is 0.1

[Guest]

1.) A utility company had to run electrical poles 10 miles between town A and town B over a hill. They discovered that the railroad company was also running a track from town A to town B but was making a level cut through the hill that would make their track 9 miles long. The utility company decided to run their poles alongside the level track, through the hill, instead over it. The utility poles need to be 99 feet apart. How many poles did the utility company save be running them alongside the track and not over the hill?

2.) There is a particular village in Madagascar that lies in a very low valley and yet at noon the sun is over 3,000 miles closer to the inhabitants of this village then when it either rises or sets. What part of the country must the village be in?

3.) If the end of the world were to occur on the first day of a new century sometime in the next 2000 years, what are the chances that it will happen on a Sunday?

4.) Leading up to a temple in Nepal there is a stairway with eight steps, not counting the landings, and the monks who worship there have a curious ritual. They start from the bottom and step onto the top landing twice (having to finish there) and return to the bottom landing once being careful to step on each step the same number of times. They always do this in the least number of steps. How many steps do the monks take?

Zero. Assuming we're going by the years 2100, 2200, 2300, etc. through 4000 (the last century before 4009, 2k years from now), the pattern goes as follows:

2100 F

2200 W

2300 M

2400 Sa

Due to 2400 being a leap year, 1 Jan 2500 resets the cycle, beginning with Friday. The cycle repeats a total of four times, and only those four days are used. We won't ever hit a Sunday using years that end in 00.

If we go by the years 2201, 2301, 2401, 2501, etc. (given that some people believe the centuries begin on the 1's, vice the 0's due to there being no year 0), the chances are still zero. Pattern as follows:

2101 Sa

2201 Th

2301 Tu

2401 M

Remember, 2400 is a leap year, as is 28, 32, etc. From this point on, the cycle repeats four more times, never falling on a Sunday.

Edit: Changed a typo'd number and a forgotten word.

Edited March 20, 2009 by Inzuri

[Guest]

i got

53.3333

1 in 7

24

[Guest]

Looking at other plps post i see im just not thinking enough

[Guest]

Zero.

I had no idea leap years were skipped in years divisible by 100, except those divisible also by 400.

edit: butterfingers...

Edited March 20, 2009 by d3k3

[Prof. Templeton]

When I originally heard this question, the answer given was that a new century would never start on a sunday (and two other days if I remember), but much later I read that a sunday would be the first day of a new century sometime in the 5th millenia.

Recapping...

2.) I was looking for anywhere.

Spoiler for because:

the Earth's radius is almost 4,000 miles, as bonanova stated, so pretty much everywhere the sun is closer at noon by over 3,000 miles (well, as you get toward the poles it's no longer true).

3.) 0% chance of a sunday for at least another 2,000 years.

4.) 19 steps.

Spoiler for the steps:

1,B,1,2,3,2,3,4,5,4,5,6,7,6,7,8,T,8,T

No one's got No.1, however. I give a hint later on if it's still open.

[Guest]

it would be 1/7

[Prof. Templeton]

it would be 1/7

Do you mean that to be the answer for No.3?

[Guest]

Is the answer 0? I think there's logic to my answer but I keep confusing myself haha.

[Prof. Templeton]

Is the answer 0? I think there's logic to my answer but I keep confusing myself haha.

That's the answer I'm looking for. Good job!

Imagine those 480 poles running alongside the level track cutting through the hill. They are 99 feet apart. Now image the same poles are long enough to extend upward above the profile of the hill. If we were to look at the profile of the hill from a distance you wouldn't see the track cutting through it just the hill and the poles extending above the surface. They are still 99 feet apart. Of course from the top of one pole to the top of another would be more then 99 feet, but still, if you measure from one pole to the next using a level it would be 99.

[Guest]

That's the answer I'm looking for. Good job!

Imagine those 480 poles running alongside the level track cutting through the hill. They are 99 feet apart. Now image the same poles are long enough to extend upward above the profile of the hill. If we were to look at the profile of the hill from a distance you wouldn't see the track cutting through it just the hill and the poles extending above the surface. They are still 99 feet apart. Of course from the top of one pole to the top of another would be more then 99 feet, but still, if you measure from one pole to the next using a level it would be 99.

Yayyy, that's what I thought! My first post and I got one right, feels good haha. I've been checking this place out for like two weeks and decided I should participate.

[bonanova]

That's the answer I'm looking for. Good job!

Imagine those 480 poles running alongside the level track cutting through the hill. They are 99 feet apart. Now image the same poles are long enough to extend upward above the profile of the hill. If we were to look at the profile of the hill from a distance you wouldn't see the track cutting through it just the hill and the poles extending above the surface. They are still 99 feet apart. Of course from the top of one pole to the top of another would be more then 99 feet, but still, if you measure from one pole to the next using a level it would be 99.

Well, maybe, but ... by whatever means it was determined to be 10 miles to the town, it would also be determined that your poles are 110 feet apart. If you wired on poles along the track, then used the same wire and poles along the hill, the wire, at 99 feet per pole, would not reach the town.