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# So you think ur smart?

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• 18-07-2008 12:21am
Registered Users Posts: 19,705 ✭✭✭✭

One:

A scientist is experimenting with bacteria that are one micron in diameter and that reproduce by dividing every minute into two bacteria. At 12:00 PM, he puts a single organism in a container. At precisely 1:00 PM, the container is full.

At what time was the container half full?

How big was the container?

Two:

An investor trading through a discount stock broker that charges \$10.00 Dollars per transaction bought 200 shares of Vola Tile Corporation at \$50.00 Dollars per share. The stock quickly increased in value by 50%, but then lost 40% of its value. The investor sold the stock.

How much money did the investor gain or lose?

and Finally:

A valuable painting was stolen from the Liar's Club, but the police are having a hard time identifying the culprit because every statement made by a member of the Liar's Club is false. Only four members visited the club on the day that the painting was stolen. This is what they told the police:

Ann: None of us took the painting. The painting was here when I left.
Bob: I arrived second. The painting was already gone.
Chuck: I was the third to arrive. The painting was here when I arrived.
Tom: Whoever stole the painting arrived before me. The painting was already gone.

Who of these four liars stole the painting?

One and two might be easy - but 3 - well that will seperate the men from the boys

## Comments

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#2
Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,090 Mod ✭✭✭✭

1:
2^60 = 1, 152, 921, 504, 606, 846, 976 it was half full at 12:59pm. Although the bacteria occupy a volume of 1×10^-12 cubic centimeters(1 micron). This would imply that the bacteria are cubic but the question says they are sperical, 1 micron in diameter. This changes the way they pack and the answer. It would be about a cubic metre in size ie a micron x 1, 152, 921, 504, 606, 846, 976.

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#3
Posts: 0 ✭✭✭✭

Ace2007 wrote: »
One:

A scientist is experimenting with bacteria that are one micron in diameter and that reproduce by dividing every minute into two bacteria. At 12:00 PM, he puts a single organism in a container. At precisely 1:00 PM, the container is full.

At what time was the container half full?
12:59

How big was the container?
1,152,921,504,606,846,976 microns

Two:

An investor trading through a discount stock broker that charges \$10.00 Dollars per transaction bought 200 shares of Vola Tile Corporation at \$50.00 Dollars per share. The stock quickly increased in value by 50%, but then lost 40% of its value. The investor sold the stock.

How much money did the investor gain or lose?
Lost 1020
and Finally:

A valuable painting was stolen from the Liar's Club, but the police are having a hard time identifying the culprit because every statement made by a member of the Liar's Club is false. Only four members visited the club on the day that the painting was stolen. This is what they told the police:

Ann: None of us took the painting. The painting was here when I left.
Bob: I arrived second. The painting was already gone.
Chuck: I was the third to arrive. The painting was here when I arrived.
Tom: Whoever stole the painting arrived before me. The painting was already gone.

Who of these four liars stole the painting?

i'm too tired after work to do this one!

..

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#4
Registered Users Posts: 2,764 ✭✭✭

Obvious answer Ann??

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#5
Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,090 Mod ✭✭✭✭

oh, 1020 for the second, I was charging 10\$ a share at first, not transaction.

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#6
Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,090 Mod ✭✭✭✭

Third one took a while as I had to figure out if they could be there at the same time and so on, since it is impossible to figure out that way I have logically concluded the order of their arrival with ann arriving 3rd and the painting still being there but when she left it was gone so it was her. I also thought it might be her from the start since she said that one of them did not take the painting, therefore one of them did, and since she knew one of them did it had to be her. But still, had to work it out logically. :-pEDIT: It could have been tom wither, there is a mistake in logic which makes it unsolvable unless you take what they say in a very specific way, ie tom said that the thief was there before him, this does not mean that they arrived after him, it could have been him.

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#7
Registered Users Posts: 5,398 ✭✭✭

1) 2^60 - w/e that is.
12.59

2) -\$10+\$5000-\$6000-\$10= -1,020

3) Ann -

Order of Bob, Tom, Ann and Chuck.

Painting still there with bob, Still there after tom, gone when Ann left, Goen when chuck arrived.

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#8
Registered Users Posts: 2,764 ✭✭✭

I feel I should have answered the other two
as well but it had already been done

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#9
Banned (with Prison Access) Posts: 218 ✭✭

Go to disagree with Joe. Agree with Tara - not enough information for #3 (or depends on a very specific interpretation)

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#10
Closed Accounts Posts: 3,441 ✭✭✭

1.

2^59 not 2^60
12.59 its half full

2.

-10-(200*50)+((200*(50*1.5)*0.6))-10 = -1020

3.

:pac:

The only person i can eliminate is chuck so i think the other three did it together.

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#11
Registered Users Posts: 19,705 ✭✭✭✭

so the first 2 were easy enough, but for the third one, the answer was Ann as a few people have said - here's why step by step

Since every statement is false, let us convert them into true statements, and number each statement:

Ann: 1) One of us took the painting. 2) The painting was gone when I left.
Bob: 3) I arrived first, third, or fourth. 4) The painting was still here.
Chuck: 5) I arrived first, second, or fourth. 6) The painting was gone when I arrived.
Tom: 7) Whoever stole the painting arrived after me. 8) The painting was still here.

According to statement #7, Tom is not the thief. #8: Since the painting was there when Tom arrived, he could not have been the last to arrive. Tom must have gone there first, second, or third. #6: The painting was gone when Chuck was there, so he didn't arrive first. #5: So Chuck got there second or fourth. #4 and #8: As two other members (Bob and Tom) arrived to see the painting, Chuck didn't get there second, either. So Chuck arrived fourth. #3: This means Bob arrived first or third. #2: Since the painting was gone when Ann left, she didn't arrive first. Otherwise, no member after her would have seen the painting. So Ann went there second or third and Chuck arrived fourth. But since two other members (Bob and Tom) saw the painting when they arrived, Ann didn't go there second, either. So Ann arrived third. #3: Therefore, Bob arrived first, and Tom arrived second.

In summary, Bob arrived first. Tom got there next and the painting was still there, so Bob was not the thief, and neither was Tom. When Ann arrived, the painting was still there, but it was gone when she left. So Ann was the one who stole the painting. Chuck arrived last and discovered that the painting was gone.

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#12
Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,090 Mod ✭✭✭✭

Unless of course tom took it, nothing to say he did not.

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#13
Registered Users Posts: 2,534 ✭✭✭

Painting still there with bob, Still there after tom

You can't deduce that - you can say that
the painting was there when Tom arrived
, but not necessarily
still there when he left
.
Ace2007 wrote: »
When Ann arrived, the painting was still there

Don't know where you're getting that from. You can say it was gone when she left, but not necessarily that it was there when she arrived.

Clearly Tom and Ann are in cahoots!

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#14
Registered Users Posts: 670 ✭✭✭

Ace2007 wrote: »
so the first 2 were easy enough, but for the third one, the answer was Ann as a few people have said - here's why step by step

Since every statement is false, let us convert them into true statements, and number each statement:

Ann: 1) One of us took the painting. 2) The painting was gone when I left.
Bob: 3) I arrived first, third, or fourth. 4) The painting was still here.
Chuck: 5) I arrived first, second, or fourth. 6) The painting was gone when I arrived.
Tom: 7) Whoever stole the painting arrived after me. 8) The painting was still here.

According to statement #7, Tom is not the thief. #8: Since the painting was there when Tom arrived, he could not have been the last to arrive. Tom must have gone there first, second, or third. #6: The painting was gone when Chuck was there, so he didn't arrive first. #5: So Chuck got there second or fourth. #4 and #8: As two other members (Bob and Tom) arrived to see the painting, Chuck didn't get there second, either. So Chuck arrived fourth. #3: This means Bob arrived first or third. #2: Since the painting was gone when Ann left, she didn't arrive first. Otherwise, no member after her would have seen the painting. So Ann went there second or third and Chuck arrived fourth. But since two other members (Bob and Tom) saw the painting when they arrived, Ann didn't go there second, either. So Ann arrived third. #3: Therefore, Bob arrived first, and Tom arrived second.

In summary, Bob arrived first. Tom got there next and the painting was still there, so Bob was not the thief, and neither was Tom. When Ann arrived, the painting was still there, but it was gone when she left. So Ann was the one who stole the painting. Chuck arrived last and discovered that the painting was gone.

Your logic seems to use two assumptions that none of the members' visits overlapped and that if a statement is false, then the opposite is true. Leaving these out of the question makes in unsolveable in my opinion. e.g. Tom saying the thief arrived after him being false does not necessarily mean that the thief arrived before him, he could be the thief himself and the original statement would still be false.

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#15
Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,090 Mod ✭✭✭✭

Thanks for agreeing with me everybody. :pac:

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#16
Closed Accounts Posts: 107 ✭✭

1. assuming the bacteria are of a circular shape regardless of how that shape fluxuates it will still have the same area therefore the size of the container is:

(2^60)Pi

For every minute that passes you increase the power by one.To begin there is one bacteria present so is represented by 2^0. After 1 minute the number of bacteria is 2 or otherwise 2^1. After 60 mins the number of bacteria is 2^60 or 8192.
Every bacteria is one micron in diameter so the resulting area is then Pi*d or Pi*1 microns^2

therefore after 60 mins the total area of the microns is equal to the total area of the container which is: 8192*Pi microns^2

2. someone up above has this correct already answer is -1020

3. Cant be Chuck painting wasn't there when he arrived.
Ann is a grey area however examining the exact phrasing (or more the opposite of) we can assume the painting was stolen BEFORE she left.
Tom and Bob are the only likely suspects because the painting was present when they both arrived however I'm more inclined to believe Bob stole it simply because reversing Toms statement in the literal sense indicates the painting was there when he arrived but the culprit arrived after him. This satisfies the reverse statement of Bobs which claims the painting was there when he arrived and that he either arrived 1st, 3rd or last. It fits the story if he arrived 3rd. Ann 1st arrived, Tom next, Bob (painting stolen), Ann leaves, Chuck arrives!!

please correct me if im wrong theres nothing i love more than heated logical debate!!

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#17
Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,090 Mod ✭✭✭✭

1. assuming the bacteria are of a circular shape regardless of how that shape fluxuates it will still have the same area therefore the size of the container is:

(2^60)Pi

For every minute that passes you increase the power by one.To begin there is one bacteria present so is represented by 2^0. After 1 minute the number of bacteria is 2 or otherwise 2^1. After 60 mins the number of bacteria is 2^60 or 8192.
Every bacteria is one micron in diameter so the resulting area is then Pi*d or Pi*1 microns^2
therefore after 60 mins the total area of the microns is equal to the total area of the container which is: 8192*Pi microns^2
They may not be circular as a micron implies they are cubic. :-)
They amy pack in different ways.
3. Cant be Chuck painting wasn't there when he arrived.
Ann is a grey area however examining the exact phrasing (or more the opposite of) we can assume the painting was stolen BEFORE she left.
Tom and Bob are the only likely suspects because the painting was present when they both arrived however I'm more inclined to believe Bob stole it simply because reversing Toms statement in the literal sense indicates the painting was there when he arrived but the culprit arrived after him. This satisfies the reverse statement of Bobs which claims the painting was there when he arrived and that he either arrived 1st, 3rd or last. It fits the story if he arrived 3rd. Ann 1st arrived, Tom next, Bob (painting stolen), Ann leaves, Chuck arrives!!

please correct me if im wrong theres nothing i love more than heated logical debate!!
There is a mistake in logic in the question, the answer can be either tom or ann, nobody else.
If you take it that the sentences have to be the opposite of what is said, Ann is the only answer.
This all asssumes they can not be there at teh same time, as this would make it unsolvable.

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#18
Closed Accounts Posts: 107 ✭✭

They may not be circular as a micron implies they are cubic. :-)
They amy pack in different ways.

There is a mistake in logic in the question, the answer can be either tom or ann, nobody else.
If you take it that the sentences have to be the opposite of what is said, Ann is the only answer.
This all asssumes they can not be there at teh same time, as this would make it unsolvable.

I was not aware a micron was cubic! My mistake! Wouldn't that still mean though that the volume of the container is Pi*(16,777,216) microns^3??
that being the Pi*r^2 formula.

Also I wasnt exactly reversing their statements, at least not intentionally i just happened to write it like that, in my own mind i was taking each of their statements as being "not true" and so processed through the remaining probabilities that could have arisen and arrived at that conclusion.

Thanks for correcting me!! haha!!

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#19
Moderators, Science, Health & Environment Moderators, Social & Fun Moderators, Society & Culture Moderators Posts: 60,090 Mod ✭✭✭✭

Well a micron itself is just a tiny amount of length but the way it is phrased makes it look cubic. Answer is2^60 x 1 micron(one millionth of a metre).
Micron has not existed since 1968 though, it is a micrometer now.

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