Dadpad:
Q4 fleas have eight legs therefore not an insect.
I have Tick - I will have to double check.
Q5 Brownian motion..... except that temparature differentials act on the water molecules to increase/ decrease pressure on the single celled creature. So newtons law of inertia has a role here. (I think?)
'Therefore you are'
Q6 Trypanosome gambiense watch out for this one its nasty
Goodonyah mate. Do you know Vic from ?'big pond'?
Mark:
EIGHT-DIGIT NUMBER
94122353 (it's unique)
Continue to let "^" denote exponentiation.
The solution is obtained by considering 10000B + C = B^2 +C^2,
Rewriting this as 10000^2 +1 = (2*B-10000)^2 +(2*C-1)^2,
Just look at the factorization of 10000^2 + 1 = 10^8 +1 = 17 *5882353.
Express each prime factor as the sum of squares:
17 = 4^2 + 1^2 = w^2 + x^2;
5882353 = 588^2 + 2353^2 = y^2 + z^2.
Then combine them according to the usual laws (related to the multiplication of complex numbers):
(w^2 + x^2)(y^2 + z^2) = (wy+xz)^2 + (wz-xy)^2
(w^2 + x^2)(y^2 + z^2) = (wy-xz)^2 + (wz+xy)^2
The second equation gives an uninteresting solution. The first gives us 4705^2 + 8824^2. Since 2C-1 is odd and 2B-10000 is even, we know which is which. 2C-1=4705 so that C=2353, and 2B-10000=8824 (or -8824) so that B is 9412 (or 588).
B=588 is ruled out by demanding a strict 8-digit number. So the answer is B=9412, C=2353, N=94122353.
HAPPINESS
two thirds wine, one third cigars
Let U=happiness.
U=w2*c.
3*w + 2*c = 100.
c=(100-3w)/2.
U=w2*(100-3w)/2.
dU/dw=2w*(100-3w)/2 + w2*-3/2=0.
Solving for w yields w=200/9.
With wine costing $3 a glass this will cost 3*200/9=$66.67, leaving $33.33 for cigars, for which he can buy 16.67.
We don't advise excess drink and smoking.
FOUR BALLS / URN
9 (via simulation)
"I hope you publish the ?'proper' way to solve the urn/balls problem."
I don't know about ?'proper' but hope springs eternal. I kinda like your way.
Call the four colors 1,2,3, and 4.
After the first turn you will have a configuration like 1,1,2,3. Call this configuration 1.
From configuration 1 if you draw a 1 on the first ball you will end up with the same or similar configuration. The probability of this happening is 1/2.
From configuration 1 if you draw a 3 or 4 first and then a 1 you will have a configuration like 1,1,1,2. The probability of this happening is 1/3. Call this new pattern configuration 2.
From configuration 1 if you draw a 3 or 4 first and then draw the other non 1 you will have a configuration like 1,1,2,2. The probability of this is 1/6. Call this new pattern configuration 3.
From configuration 2 you will end up with the same pattern with probability 1/2, configuration 3 with probability 1/4, and ending the experiment with probability 1/4.
From configuration 3 you will end up with the same thing with probability 1/3, and with configuration 2 with probability 2/3.
From this information you can draw the following equations, where a is the expected number of turns from equation 1, b from equation 2, and c from equation 3:
a=(a+1)/2 + (b+1)/3 + (c+1)/6
b=(b+1)/2 + (1)/4 + (c+1)/4
c=(c+1)/3 + (2/3)*(b+1)
Finally simple matrix algebra will show a=8. Considering the first turn from the original condition to equation 1 the expected number of turns is 9.
Olive in the glass no more.
I hope you did not get any paint on your clothes during your trials.
I once went to watch the sheepdog trials - they were all found guilty.
Now, this question should cause a bit of a discussion.
A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads what is the probability that the other side is heads
Q 7:
You continue to shrink until you are the size of a virus. Which of the following diseases is NOT caused by a virus
Mumps
Influenza
Measles
Dysentery
Q 8:
You become much, much smaller, until you can start to see individual molecules. Mixed in with all the water molecules surrounding you, you see a molecule which consists of a single carbon atom connected to three hydrogen atoms, and also connected to an oxygen atom, which is connected to another hydrogen atom. What substance is made up of these molecules
Benzene
Ethanol
Methanol
Acetone
Mark, could you please explain how you moved from/to:
react
nectar
With one move/change ?
I am still working on it.
