Mind benders!, Now with polling goodness!! Options

[Pahzy See]

Here's a couple mental exercises to keep you alert.

1. If seven men can dig twenty-one holes in nine days, how long will it take five men to dig twenty holes of the same size?

2. With a seven minute hourglass and an eleven minute hourglass, what is the quickest way to time the boiling of an egg for fifteen minutes?

This post has been edited by Pahzy See: Aug 9 2010, 03:07 PM

[Naught_Wright]

Here's a couple mental exercises to keep you alert.

1. If seven men can dig twenty-one holes in nine days, how long will it take five men to dig twenty holes of the same size?
Assuming an identical rate of work, twelve days.

2. With a seven minute hourglass and an eleven minute hourglass, what is the quickest way to time the boiling of an egg for fifteen minutes?
Start both hourglasses at the same time while bringing the water to a boil (not the egg). When the seven-minute timer runs out drop in the egg. Wait out the rest of the sand in the eleven-minute timer, then flip it. When it empties again your egg will be perfect. Total time: 22 minutes.

[Pahzy See]

1. If seven men can dig twenty-one holes in nine days, how long will it take five men to dig twenty holes of the same size?
Assuming an identical rate of work, twelve days.

Correct!: The rate is specifically 1 man can dig 1 hole in 3 days

2. With a seven minute hourglass and an eleven minute hourglass, what is the quickest way to time the boiling of an egg for fifteen minutes?
Start both hourglasses at the same time while bringing the water to a boil (not the egg). When the seven-minute timer runs out drop in the egg. Wait out the rest of the sand in the eleven-minute timer, then flip it. When it empties again your egg will be perfect. Total time: 22 minutes.

This can actually be done in less time. In fact : total time is 15 minutes when done correctly!

[Sovolis]

Correct!: The rate is specifically 1 man can dig 1 hole in 3 days

This can actually be done in less time. In fact : total time is 15 minutes when done correctly!

Naught Wright is on the right track(I think): Set both hourglasses going at the same time. When the 7 minute one runs out there will be four minutes left on the 11 minute one. Start the egg. Set the 11 minute hourglass a second time when it runs out after the first run. When the 11 minute hourglass runs out the second time the egg will be done. Total time is 22 minutes. Cooking time is 15 minutes. Of course this is what Naught Wright was saying. He was just starting the boil while both ran out. His total cooking time excluding initial boil would have been 15 minutes as well.

This post has been edited by Sovolis: May 18 2010, 10:06 AM

[Pahzy See]

Naught Wright is on the right track(I think): Set both hourglasses going at the same time. When the 7 minute one runs out there will be four minutes left on the 11 minute one. Start the egg. Set the 11 minute hourglass a second time when it runs out after the first run. When the 11 minute hourglass runs out the second time the egg will be done. Total time is 22 minutes. Cooking time is 15 minutes. Of course this is what Naught Wright was saying. He was just starting the boil while both ran out. His total cooking time excluding initial boil would have been 15 minutes as well.

The question was: What is the quickest way to time the boiling of an egg for fifteen minutes? Obviously the cooking time would be 15 minutes, or the egg would overcook!

The timing can be done in exactly 15 minutes, and this is how:

First drop the egg, and start both hourglasses at the same time.

When the 7 minute timer runs out, turn it back over. (time = 0:07)

When the 11 minuter timer runs out, turn the 7 minute timer back over again. (time = 0:11)

The 7 minute time should have 4 minutes elapsed when the 11 minute timer ran out, so when we turn it over, there will be 4 minutes left in it. When this runs out... (time = 0:15)

No additional prep time is required and seven minutes may or may not be adequate time for a decent boil. Your method does work for timing the egg correctly, but it is not quite as efficient.

[Sovolis]

The question was: What is the quickest way to time the boiling of an egg for fifteen minutes? Obviously the cooking time would be 15 minutes, or the egg would overcook!

The timing can be done in exactly 15 minutes, and this is how:

First drop the egg, and start both hourglasses at the same time.

When the 7 minute timer runs out, turn it back over. (time = 0:07)

When the 11 minuter timer runs out, turn the 7 minute timer back over again. (time = 0:11)

The 7 minute time should have 4 minutes elapsed when the 11 minute timer ran out, so when we turn it over, there will be 4 minutes left in it. When this runs out... (time = 0:15)

No additional prep time is required and seven minutes may or may not be adequate time for a decent boil. Your method does work for timing the egg correctly, but it is not quite as efficient.

Ahh, I see. I knew it was something like that. I love these kind of thought problems.

[Pahzy See]

Here's one to test your powers of observation:

A man leaves his home one morning, locks the door and proceeds to head north in search of food. After a couple of miles, the hunter gets tired and stops for a quick break. Suddenly, he hears the roar of a bear and sees a large, moving shape coming at him from the east. With barely enough time to gather his essential supplies, he quickly runs in the opposite direction the bear is charging at him from. Unfortunately the bear is slightly faster than the man and slowly begins to gain ground on him.

After about three miles into the chase, the man spots a small cabin up ahead. With every last bit of adrenaline he can muster, he sprints towards the building. As her nears the cabin, his knees begin to give way and he shouts frantically at whomever may be inside to help. No answer comes from within. The hunter collapses at the door and with only a few seconds before the bear overtakes him, he turns the handle--only to find it locked!

The bear, realizing it has its prey cornered, comes to a stop a few feet from the hunter to get a better idea how to approach him. The man, realizing that the end was near, puts his hand to his heart and prayes for a miracle. The bear begins to slowly advance on the hunter. Suddenly, the man gasps in disbelief, and within moments is safe and sound within the cabin. Frustrated, the bear sulks and walks away.

What color was the bear?

[Sovolis]

Here's one to test your powers of observation:

A man leaves his home one morning, locks the door and proceeds to head north in search of food. After a couple of miles, the hunter gets tired and stops for a quick break. Suddenly, he hears the roar of a bear and sees a large, moving shape coming at him from the east. With barely enough time to gather his essential supplies, he quickly runs in the opposite direction the bear is charging at him from. Unfortunately the bear is slightly faster than the man and slowly begins to gain ground on him.

After about three miles into the chase, the man spots a small cabin up ahead. With every last bit of adrenaline he can muster, he sprints towards the building. As her nears the cabin, his knees begin to give way and he shouts frantically at whomever may be inside to help. No answer comes from within. The hunter collapses at the door and with only a few seconds before the bear overtakes him, he turns the handle--only to find it locked!

The bear, realizing it has its prey cornered, comes to a stop a few feet from the hunter to get a better idea how to approach him. The man, realizing that the end was near, puts his hand to his heart and prayes for a miracle. The bear begins to slowly advance on the hunter. Suddenly, the man gasps in disbelief, and within moments is safe and sound within the cabin. Frustrated, the bear sulks and walks away.

What color was the bear?

Answer: White

[Pahzy See]

Answer: White

Care to explain your reasoning?

[archenemy1]

hmmm cant figure this one out at all. i have no idea.

[Sovolis]

Care to explain your reasoning?

The first paragraph states that the man locked the door. The last paragraph states that the man placed his hand on his heart and prayed for a miracle. Shortly there after he is safe and sound within the cabin. We have to assume that he found the key to his own cabin in his shirt pocket and used it to unlock the door. That would mean that this is his cabin. If that is the case we have to figure out how he could arrive back at his cabin after proceeding north and then heading east. (Assuming he maintained these headings regardless of being in a panic while heading east.) The only way this is possible is if he crossed over the north pole while heading north. That would mean that while maintaining motion in a single direction his heading would have changed from north to south after crossing the pole. If this happened he could proceed east to arrive back where he started from. That would mean the bear is a polar bear. Hence the bear would be white.


EDIT-I am guessing that something can be figured out by the fact that the man ran east for roughly 3 miles so he must have traveled on his north heading for roughly 4 miles. 2 miles in a north heading 2 miles in a south heading. If I am correct in the circumfrence of a circle being R*Pi. This isn't the way I figured it out since I am rather poor at math.

This post has been edited by Sovolis: May 18 2010, 01:10 PM

[Pahzy See]

The first paragraph states that the man locked the door. The last paragraph states that the man placed his hand on his heart and prayed for a miracle. Shortly there after he is safe and sound within the cabin. We have to assume that he found the key to his own cabin in his shirt pocket and used it to unlock the door. That would mean that this is his cabin. If that is the case we have to figure out how he could arrive back at his cabin after proceeding north and then heading east. (Assuming he maintained these headings regardless of being in a panic while heading east.) The only way this is possible is if he crossed over the north pole while heading north. That would mean that while maintaining motion in a single direction his heading would have changed from north to south after crossing the pole. If this happened he could proceed east to arrive back where he started from. That would mean the bear is a polar bear. Hence the bear would be white.


EDIT-I am guessing that something can be figured out by the fact that the man ran east for roughly 3 miles so he must have traveled on his north heading for roughly 4 miles. 2 miles in a north heading 2 miles in a south heading. If I am correct in the circumfrence of a circle being R*Pi. This isn't the way I figured it out since I am rather poor at math.

Bingo! It is my own take on the more simplied version of a man walks 1 mile south, 1 mile east and 1 mile north to end up back where he started. I decided to change the parameters slightly and embelish on the story a bit to throw the reader off. You managed to successfully focus on the important details and have earned a gold star.

Expect 6-8 weeks for delivery


As to your edit, the circumference of a circle is 2*pi*r. It was stated that he walked for a couple (2) miles heading north before heading east, not that he walked north for 2 miles. Important difference. This would mean the radius would be 1 mile, making the circumference 2*pi. Since he only had to travel half of the distance around the circle to get back to the starting point, his distance travelled would be pi, or 3.14 miles. As stated in the story, he did indeed walk 2 miles in one direction and about three in another, consistent with the geometry of the location.

Here's another one for you:


A family gathering consists of father, mother, son, daughter, brother, sister, cousin, nephew, niece, uncle, and aunt. But there are only two men and two women present. They all have a common ancestor, yet there are no marriages within the group that could be considered illegal or inappropriate. How is this possible?

This post has been edited by Pahzy See: May 18 2010, 01:24 PM

[Sovolis]

Bingo! It is my own take on the more simplied version of a man walks 1 mile south, 1 mile east and 1 mile north to end up back where he started. I decided to change the parameters slightly and embelish on the story a bit to throw the reader off. You managed to successfully focus on the important details and have earned a gold star.

Expect 6-8 weeks for delivery
As to your edit, the circumference of a circle is 2*pi*r. It was stated that he walked for a couple (2) miles heading north before heading east, not that he walked north for 2 miles. Important difference. This would mean the radius would be 1 mile, making the circumference 2*pi. Since he only had to travel half of the distance around the circle to get back to the starting point, his distance travelled would be pi, or 3.14 miles. As stated in the story, he did indeed walk 2 miles in one direction and about three in another, consistent with the geometry of the location.

It has been a long time since I took any math. I couldn't remember if circuference was 2*pi*r or pi*r. I didn't do well in math classes due to indifference regardless of the fact that I am good at math when I know what I am doing and care to do it well. I now really regret not taking math seriously and always try to get better at it. This is also why I logic'd the problem out rather than sticking to hard math.

Here's another one for you:
A family gathering consists of father, mother, son, daughter, brother, sister, cousin, nephew, niece, uncle, and aunt. But there are only two men and two women present. They all have a common ancestor, yet there are no marriages within the group that could be considered illegal or inappropriate. How is this possible?

This is a quick answer, so it may be wrong. 2 men 2 women (you told us that already) 1 man is the son of one of the women. The other woman is the daughter of the other man. The woman with the son and the man with the daughter are brother and sister.


I am going to look up a really interesting one on my phone and post it here. It is going to take me a while since I will have to type it out. (I am currently behind a firewall)

[Pahzy See]

This is a quick answer, so it may be wrong. 2 men 2 women (you told us that already) 1 man is the son of one of the women. The other woman is the daughter of the other man. The woman with the son and the man with the daughter are brother and sister.

That's it. An alternative answer would have been a man and his son, his sister and his sister's daughter.

[archenemy1]

im new here, im just wondering, why are most of the posts blacked out so i cant read them?

[Pahzy See]

im new here, im just wondering, why are most of the posts blacked out so i cant read them?

It's a spoiler tag. It basically blacks out whatever text you want so that people who do not want answers or plot devices given away can avoid accidentally reading them.

Anytime you want to read what is hidden under a spoiler tag, just left click on the start of the box and drag across the screen. You will then see the text carefully hidden beneath.

Oh, and welcome!

[archenemy1]

It's a spoiler tag. It basically blacks out whatever text you want so that people who do not want answers or plot devices given away can avoid accidentally reading them.

Anytime you want to read what is hidden under a spoiler tag, just left click on the start of the box and drag across the screen. You will then see the text carefully hidden beneath.

Oh, and welcome!

Oooh i see! Thank you so much, i thought maybe i didnt set up my acct right and i had limited access lol.

thank you, this website is great

[Sovolis]

Lost on the Moon Worksheet
from NASA

Your spaceship has just crashed on the moon. You were scheduled to rendezvous with a mother ship 200 miles away on the lighted surface of the moon, but the rough landing has ruined your ship and destroyed all the equipment on board except for the 15 items listed below.

Your crew's survival depends on reaching the mother ship, so you must choose the most critical items available for the 200-mile trip.

Your task is to rank the 15 items in terms of their importance for survival. Place a number 1 by the most important item, number 2 by the second most important, and so on, through number 15, the least important.

• Box of Matches
• Food Concentrate
• 50 feet of nylon rope
• Parachute silk
• Solar-powered portable heating unit
• Two .45caliber pistols
• One case of dehydrated milk
• Two 100-pound tanks of oxygen
• Stellar Map (of the moon's constellations)
• Self-inflating life raft
• Magnetic compass
• 5 gallons of water
• Signal flares
• First-aid kit containing injection needles
• Solar-powered FM receiver-transmitter

Error points are the difference between your rankings and NASA's (disregarding plus or minus signs).

0-25 excellent
26-32 good
33-45 fair
46-55 bad
56-70 oops
71-112 oh, well


*I will score a few entries out before revealing the ranks NASA assigns*

[Pahzy See]

Your task is to rank the 15 items in terms of their importance for survival. Place a number 1 by the most important item, number 2 by the second most important, and so on, through number 15, the least important.

[1] Two 100-pound tanks of oxygen - critical
[2] 5 gallons of water - critical
[3] Food Concentrate - obviously important for sustenance
[4] Stellar Map (of the moon's constellations) - necessary for navigation
[5] Solar-powered FM receiver-transmitter - useful for contact with mother ship
[6] 50 feet of nylon rope - may come in handy
[7] First-aid kit containing injection needles - may be necessary in case of injury
[8] Parachute silk - protection from the sun
[9] Signal flares - may help in aletring aid
[10] Self-inflating life raft - shelter/propulsion
[11] Two .45caliber pistols - mostly useless (possible use for propulsion)
[12] One case of dehydrated milk - unnessecary with food concentrate
[13] Magnetic compass - useless on the Moon
[14] Solar-powered portable heating unit - useless
[15] Box of Matches - useless

[Sovolis]

[1] Two 100-pound tanks of oxygen - critical
[2] 5 gallons of water - critical
[3] Food Concentrate - obviously important for sustenance
[4] Stellar Map (of the moon's constellations) - necessary for navigation
[5] Solar-powered FM receiver-transmitter - useful for contact with mother ship
[6] 50 feet of nylon rope - may come in handy
[7] First-aid kit containing injection needles - may be necessary in case of injury
[8] Parachute silk - protection from the sun
[9] Signal flares - may help in aletring aid
[10] Self-inflating life raft - shelter/propulsion
[11] Two .45caliber pistols - mostly useless (possible use for propulsion)
[12] One case of dehydrated milk - unnessecary with food concentrate
[13] Magnetic compass - useless on the Moon
[14] Solar-powered portable heating unit - useless
[15] Box of Matches - useless

Very well done.

Your score is 6.

Incidently this is the best score I have ever seen on this test.

I can't recall exactly what my score was but I think it was in the 12-14 range. May have been as high as 19 or 20. It was about a year ago that I first took the test.

Edit-I added the spoiler tag to hide your score. That way people wont get an unfair advantage or disadvantage.

This post has been edited by Sovolis: May 18 2010, 03:10 PM