Tricky Questions

[Steve]

Answer: A sponge....

only thing I can see holey undewear being usefull is airing out your down under on a hot summer day

Hmm...kind of a flawed riddle, isn't it? A sponge is only useful when it's EMPTY...if its full, you can't soak anything up.

 

[TinyKilbasa]

didnt think about that....good point

 

[Ames]

Have you ever though that "The Thing" might just google your question and get the answer automaticaly?

No...

/me waves riddle books..

 

[Dan]

For DAN (message 151):

You only have to ask 11 questions if you use the form:

Is the remainder of "number" / 2 >= 1?
Is the remainder of "number" / 4 >= 2?
Is the remainder of "number" / 8 >= 4?
...
Is the remainder of "number" / 1024 >= 512?
Is the remainder of "number" / 2048 >= 1024?

(This gives you the number in binary...each question represents a bit)

but what if he lies? Remember that he may or may not lie about one of his answers. But you are on the right track

 

[Dan]

and for the mountain climber one they are the first to climb the mountains because the other dead guys crashed there from the sky. As for the rock question, it all depends on the density of the rock/backpack combination and the shape/weight of the boat. By throwing the rock and backpack you are raising the water level by adding the volume of the rock and backpack. But you are also lowering it because the boat will now sit higher, displacing less water. It can all be calculated with simple physics and some densities

 

[NetWarriorDan]

On the boat the rocks will displace the amount of water equal to their weight. In the water they will displace their own volume. The rocks will sink which means the rocks are denser then the water. The rocks will displace more water with their weight then with their volume. The water level will go lower with the rocks in the water.

 

[Dan]

Ok here's a killer problem. There are two integers, x and y, such that x<y and 2<x+y<100. There are two logicians that are never wrong and never lie, Paddy and Susan. Paddy knows the product of x and y. Susan knows the sum of x and y. They have this conversation:

Susan: You don't know what x and y are
Paddy: Yes I do
Susan: Me too

What are x and y?

 

[Dan]

sorry, I should ammend that slightly, 1<x<y. It does make a difference. I guess that's a hint of sorts.

 

[Revisedsoul]

i know it has to do with the wording that paddy is never wrong and susan never lies. but im stuck in the conversaton

 

[Dan]

no, those are just two synonyms to mean that what they say is true.

 

[Revisedsoul]

if what they both say is true then one has to be lying cuz susan stated that paddy didnt know x and y, and paddy said she did

 

[Dan]

nope, they are both telling the truth. And because of that fact, you can deduce x and y

 

[Seeky]

The numbers are 2 and 19

Patty knew the sum, 21. Susan knew the product, 38. Susan knew that the values had to be 2 and 19.

Susan knew the sum, 21. This could be 2 + 19, 3+18, 4+17...up to 10+11. Let's look at all the products:

2 * 19: 38 (factors, 2 * 19)
3 * 18: 54 (factors, 2 * 27, 3 * 18, 6 * 9)
4 * 17: 68 (factors, 2 * 34, 4 * 17)
5 * 16: 80 (factors, 2 * 40, 4 * 20, 5 * 16, 8 * 10)
6 * 15: 90 (factors, 2 * 45, 3 * 30, 5 * 18, 6 * 15, 9 * 10)
7 * 14: 98 (factors, 2 * 49, 7 * 14)
8 * 13: 104 (2 * 52, 4 * 26, 8 * 13..)
9 * 12: 108 (2 * 54, 3 * 36, 4 * 27, 9 * 12...)
10 * 11: 110 (2 * 55, 5 * 22, 10 * 11...)

Clearly, in all cases, there are at least two ways to generate the same product. The only value where the factors are unquestionable, is if 2 * 19 is 38. Susan is not sure if Patty is aware of this, so she asks her if she knows what the factors are.

Patty states that she does - she knows the product is 38, and that the only two factors that satisfy x < y and x > 1, is 2 * 19.

Sally realizes that Patty's product must be 38, because with no other number would she be aware of the values. Sally then correctly deduces that her sum, 21, must be the sum of 2 and 19.

There are other combinations that will generate a number where Patty will be aware of the x and y value (such as 16 - it must be 2 * 8). However, there doesn't seem to be another circumstance where Sally can correctly deduce the x and y value, from realizing that Patty is cognizant of her own.

2 and 19 work.

 

[Seeky]

Solution to the bridges problem (calculus for best answer)

Assume the optimal design follows the one shown in the picture http://students.washington.edu/ckjy/islands1.JPG (which I mentioned as a hint).

Assume that the optimal equation assigns the center vertical line, a value of x. The gap above and below X are the same, (10 - x) / 2. For instance, if X is 5, then the gap above and below must be (10 - 5) / 2 = 2.5. ---- 2.5 + 2.5 + 5 = 10.

However, we want to solve for X. The total cost of the system willl be:

X + (4 * sqrt[((10 - x) / 2)^2 + (5^2)].

The first term is the X in the center. The 4 represents the symmetery of the four diagonal lines. The final terms represent the pythagorean theorem, c^2 = a^2 + b^2, where a^2 is the height of the gap, and b^2 is the horizontal distance, which will always be (because we are only varying the vertical distance).

So, let c = x + (4 * sqrt[(x^2 / 4) - 5x + 50]) (the above multiplied out).

We want to minimize cost, so we take the derivative of c with respect to X.

dc/dX = (4 * (.5[x^2 / 4 -5x + 50]^-.5) * ((x / 2) - 5) + 1 = 0.

Let's rearrange this to something easier to read, and solve for x.

((x - 10) / sqrt[(x^2 / 4) - 5x + 50] ) + 1 = 0.

You can solve this by hand, with Newton's method, or just plug it into a calculator to solve for x. You could also multiply it all out and use the quadratic formula, but that's a little messy for this purpose.

If you solve for X, you will find that x = 4.2264973.

Total cost, using x = 4.2265:
27.320525

Total cost using same design, x = 5:
27.3604.

Total cost using two diagonal X's (x variable = 0):
28.284

A significant savings.

And so, calculus is useful after all.

 

[Farrowlesparrow]

Please can you stop making multiple posts in a row.

Use the edit button.

 

[Dan]

It seems I can only edit posts for a certain amount of time after they're posted, sorry.
Anyways, as for Seeky's answer, remember it's Paddy-knows product, Susan knows sum. If it was 19 and 2, making the sum 21. Susan could not make the statement that Paddy does not know what x and y are. Remember, she doesn't ask Paddy if he knows it, she states that he doesn't know x and y. Because if x and y are 19 and 2, then the product is 38 as you say and the only proper set of factors for 38 are 19 and 2. (1 and 38 is out of the range) Therefore Paddy would immediately be able to deduce what x and y are. Because Susan is always right, she would not make the statement that Paddy doesn't know x and y unless she was 100% sure of it.
But good job on the islands problem, I can't argue with that one.