The worlds first riddle!

markr:


You're not missing anything. JARS: 1 Liter

/JARS, revisited/
Same as <JARS> but now all the jars are different sizes.

Thoh:


BEE

The trains will collide in 150/(75+75) or 1 hr.

Fast bee: in that time the bee will fly 137.5 miles

Slow bee:
Case 1: its too slow and gets hit by the train and so it 'flies' glued to the windshield for 75miles
Case 2: the bee flies out of the way and flies along the track for 37.5 miles at which point the trains collide 37.5 miles away but the bee lives.



So the bee travels (137.5) x (150/212.5) miles or approximately 97.058823 miles when it reaches the train and turns around.
(Distance = Rate x Time)
Meanwhile, the first train has traveled a distance of 75 x (150/212.5) miles or about 52.94 miles.
(Distance = Rate x Time)
Therefore, the distance between the bee and the first train is
(137.5)x(150/212.5) - 75x(150/212.5) or approximately 97.0588 - 52.94 = 44.11 miles.
In factored form, the distance would be
(150/212.5) x (137.5 - 75) miles.
When the bee is traveling back toward the first train, that train and the bee are travelling at a combined rate of 212.5 mph, so the time it will take for them to meet will be
(150x(137.5 - 75)) / (212.5 x 212.5) hours or
approximately .20761 hours.
(Time = Distance / Rate)
So the bee travels a distance of
137.5 x (150x(137.5 - 75)) / (212.5 x 212.5)
miles or approximately 28.5467 miles.
(Distance = Rate x Time)
Continuing in the same manner, you would get the following series:
97.05882352941177
28.546712802768166
8.396092000814166
2.469438823768872
0.7263055364026094
0.21361927541253217
0.06282919865074475
0.01847917607374846
0.005435051786396606
0.001598544643057825
0.0004701601891346544
0.000138282408569016
0.00004067129663794589
...


137.5 miles
I don't know how John von Neumann was able to keep all that in his head!

Another way to solve this problem is to use the formula for the sum of an infinite geometric series:
Sum = a1 / (1-r)

where a1 is the first term of an infinite geometric series, and r is the ratio between any two terms of the series (as long as r is less than 1).

Use the information above to determine what the infinte series of successive distances travelled by the bee would look like.
From step (2), the first term, or a1, equals
(137.5) x (150/212.5) miles or approximately 97.05882355.
From step (6), the second term is
(137.5) x (150/212.5) x (137.5 - 75)/212.5 or
approximately 28.5467128
Therefore, the ratio must be (137.5 - 75)/212.5
or approximately .2941176471
Substituting the values of a1 and r into the formula for the sum of an infinite series, we get:
Sum = (137.5 x (150/212.5)) / (1 - (137.5 - 75)/212.5) which equals 137.5 miles!!
Using the approximations, we get the same answer:
Sum = 97.05882355 / (1 - .2941176471) = 137.5!

Better still ask Thoh!


TTH:

The answer is: you have to be lying because if you weren't then what you said is true. With that said, it would be a lie. This is a contradiction. You can still lie about some things, this being one of them.



You have said it all. I have to be lying, because if I were not, my statement would be true, meaning it would have to be a lie, thus becoming a paradox.


An apparently ?'hunky mathematician' asked, "Are you going to share the alternate solution to the Chicago/Detroit trips?"

Strange you should mention that; that is the exact question I raised when I came outta the shower, and although I was somewhat distracted, I think the gist of what was said was that: As a result of multiple trips you accrue multiple exact crossing points regardless of the time.



ARRAY OF INTEGERS

Great question, and Mark's answer is indeed terrific. (And not one I would have come up with)





You have 64 Penguins, all of which appear identical. However, one of the Penguins is heavier than the others.

Using a (big) two-pan balance, what is the least number of weighings that you need (in the worst case) to determine the fat penguin




Mark is drinking water. Thoh is drinking tea. There are only these two drinks available. When TTH joins them, she wants something to drink too, and sees that there are just two choices. Does she drink water or tea

"As a result of multiple trips you accrue multiple exact crossing points regardless of the time."

Huh? What does that mean? What kind of proof is that?

THOH13'S JARS REVISITED
[size=8]2 liters
the jars are 1, 2, 3 liters
2 full
1, 3 half full
1,2,3 one third full[/size]

Darn and I wanted him to grovel. You always still can you know. :wink:
I am just a trivia nerd what do I know?

A little more to it than that. You better expand the box. :wink:

TTH eloquently wrote, "You better expand the box."


Ok! Mark gave Thoh a box:
About it there were many locks.
Thoh woke and said it gave him pain;
So gave it back to Mark again.
The box was not with lid supplied,
Yet caused two lids to open wide;
And all these locks had never a key-
What kind of box, then, could it be

[size=8]64 PENGUINS
4
left/right/off
27/27/10
9/9/9 (if 27/27 is balanced, then 10 can easily be reduced to 1 in three more weighings)
3/3/3
1/1/1

WATER/TEA
Since Mark insulted her, she drinks tea with Thoh.

BOX
I'm guessing the locks are hair and the two lids are eyelids. However, I don't know what the box is. Sounds like a trivia question...[/size]

Markr:


Two liters sure is the answer.

/THE STRONG BOX/
And speaking of boxes. Mark wants to send Try some diamonds. To make sure no one opens the box while in transit, he wraps a chain around it and secures it with a padlock. He doesn't want to send the key for fear it might get stolen. How does Try open his package? (sorry, no saws or torches allowed)

Mark:

WATER/TEA
Since Mark insulted her, she drinks tea with Thoh.

(Sounds like a trivia question...)


You are so right!!!


BOX
I'm guessing the locks are hair and the two lids are eyelids . However, I don't know what the box is.

This is one of the most famous Lewis Carroll Riddles: The ?'Box' as in Boxing, refers to a punch to the head. The other parts you correctly identified.


64 PENGUINS

4
left/right/off
27/27/10
9/9/9 (if 27/27 is balanced, then 10 can easily be reduced to 1 in three more weighings)
3/3/3
1/1/1


Very clever!

Another way to solve this in only four weighings is to:
Divide the Penguins into groups of 21, 21, and 22 Penguins.
Weigh the two groups of 21.
If one pan dips, then the fat penguin must be in that pan.
If the two pans balance, then fatso must be in the group of 22.
Take the group with the heavier penguin and split into 3 groups: 7, 7, and 8 (or 7).

Weigh two groups of 7. If they balance, fatso is in the other group. If the pan dips, he is in that group of Penguins.

Take the group of 7 (or 8) Penguins and split into three groups of 2, 2, and 3 (or 2, 3, and 3). Weigh the two equal groups of Penguins. If they balance, fatso is in the other group. If the pan dips, he is in that group.

You are now left with only 2 or 3 Penguins. Weigh two of them to determine the answer.



You can solve for up to 81 Penguins using Mark's method. (I doubt the same method can be used in relation to Polar Bears).

Split into 3 equal piles - 27, 27, 27 = 81
Weigh pile 1 vs. 2
Select the heavier or pile 3 if even.
Split into 3 equal piles - 9, 9, 9 = 27
Weigh pile 1 vs. 2
Select the heavier or pile 3 if even.
Split into 3 equal piles - 3, 3, 3 = 9
Weigh pile 1 vs. 2
Select the heavier or pile 3 if even.
Split into 3 equal piles - 1, 1, 1 = 3
Weigh pile 1 vs. 2
Select the heavier or pile 3 if even.



Quote, "Mark wants to send Try some diamonds"


That hunk sure knows how to please a girl.


THE STRONG BOX:


I was convinced there was no answer to this, when today I phoned the boatyard and wanted them to send the security key for the outboard to my agent for when the boat is hauled out for winter lay-up. The guy said it was too risky. So I said, I would send him my lock (take his off, put mine on) so when I next visited the boat I would have the key!

Back to the strong box: The same sort of thing; when I get the box I put my lock on it and send it back, Mark takes his lock off and returns it to me, as I have the key I can open it….

And what do I find…PASTE that's what! Cheapskate.





Some may find this question too easy, some too difficult. Me, I was too busy watching those puppies to give a damn!


TTH is jogging across the Pennsylvania Railroad Bridge over the Allegheny River at Kiskiminetas Junction. When she is 3/8ths of the way across, she hears a train coming from behind her. She calculates that if she keeps running, she will reach the end of the bridge at the same instant as the train.

She also calculates that if she turns around and runs back, she will reach the beginning of the bridge at the same instant as the train.

If she runs consistently at 8 mph, what is the speed of the train





This is a simple logic problem, simple that is if you have the answer. No tricks, and totally plausible. None were eaten, destroyed in mid air or on water etc.

There are a few trees in my garden. On one of them, a pear tree, there are pears (quite logical). But after a strong wind blew, there were neither pears on the tree nor on the ground. How come

TRAIN
The train is four times as fast as TTH.

PEARS
Perhaps they landed on a neighboring tree.
Perhaps there was a picnic table (or other object) under the tree, and they landed on it.
Perhaps, fearing losing your crop, you went out in the strong wind and picked them.

PEARS:

The clue is more numerical.

water/tea? I would drink water.
I don't know the real answer, but since you make tea with water, aren't you drinking the water?

PEARS
Is it a riddle that is better spoken than written (pairs vs. pears)?

Pears:

You have a few trees, the pear tree did not lose any in the wind. The other trees do not have pears. They are different trees???

Close, it is better thought of in terms of ?'pair' of pears. :wink:

Try:


I couldn't agree more. The chain part, I mean.

/SURVEY/
A national survey was conducted by a telemarketing firm. Of all the people called, only and EXACTLY 3.87343466281890869140625 % agreed to participate. What is the least number of people that could have agreed to participitate? What is the smallest number of calls that could have been made?

Tryagain, I hope you don't mind, but I just cannot resist. These are riddles with numbers involved.


markr:

1) How did Mark legally marry 3 women in WA without them dying, divorcing them or becoming legally separated?

2) If it has a quart capacity, how many quarters can you put into an empty piggy bank?

Mathematician= George Bernard Dantzig (NICE)
Do you have all the answers?

I will now go back to trivia since all this math is taxing my brain.