T3B112

I'm just going to do the easiest one because I don't understand any of the others :P

Basically, they agree to one person being the leader. Since the bulb starts are being off, all the prisoners agree so that everyone (except the leader) will turn on the switch if it is off, and if they haven't been in the room before. When the leader visits the room, he will turn the switch off. When he has turned the switch off 99 times, then he knows everyone has visited the room.

Now, I'm sure there are loads of better ways and complicated algorithms and calculations about the time, etc. it takes to do such a thing. But I stared at it for about an hour and none of it made sense to me, so I'll just post a link here just in case you want to see the complicated solutions.

This one's not a bad one for calculating time, but it kind of ends abruptly:

http://anttila.ca/michael/100prisoners/

Ahhh... I dunno, I'm really bad at this probability stuff. :(

T3B111

There are like a bajillion different solutions to this one:

There are 100 prisoners in solitary cells. There's a central living room with one light bulb; this bulb is initially off. No prisoner can see the light bulb from his or her own cell. Everyday, the warden picks a prisoner equally at random, and that prisoner visits the living room. While there, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting that all 100 prisoners have been to the living room by now. If this assertion is false, all 100 prisoners are shot. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world could always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity. The prisoners are allowed to get together one night in the courtyard, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?

T3B109

I love this song. <3 <3 <3

T3B110

OMG this song is soooo catchy it's stuck in my head. It's not even that representative of the actual movie but the tune is just soooo... AGH.

As you can see, I'm kind of back to my "FROOOOOOZEEEENNNN" obsession. :P I just found the blu-ray collector's edition at Costco and I'm like "YYYYEEESSSSSS"

T3B108

Three.

I don't know. I don't get it.

How would it be placed???

T3B107

There were two cupcakes in front of a cupcake, one cupcake between two cupcakes, and one cupcake behind two cupcakes. How many cupcakes were there?

You know, I never got this one, no matter how many times I saw it...

T3B106

When the going gets tough, the tough get going.

Haha.

It's not a bad one, just kind of confusing at first. :)

T3B105

This one is a bit difficult to decipher at first because you don't really know what they're asking.

So, for clarification, "easy going" is when the going is easy. (Did that make sense? That didn't really make sense.)

"Weak" and "Tough" refer to types of people (I think?).

Here it is:

Easy going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Medium going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Tough going:
Weak, 'I can't do it, I'm staying!'
Tough, 'Let's get going.'

T3B104

1. Back to Square One--A term meaning to go back to the beginning, or the original idea.

2. Blind leading the blind--Term which means the person in charge knows no more than the person or people he is leading.

3. Hold your Horses--Meaning be patient and to wait.

4. The pen is mightier than the sword--A phrase that means you can get more accomplished by solving your problems in a calm way, than resorting to violence.

T3B103

OMG I LOVE THESE

The following are colloquialisms/idioms written in their literal form. Try to find all four.

Example: A Panthera Pardus is incapable of altering its texture. (A leopard can't change its spots)

1. Revert to the first quadrilateral of equal sides and angles.

2. One suffering from Macular Degeneration guiding one with less than 1/10 of normal vision.

3. Restrain your multiple Equus caballus.

4. The writing utensil containing small amounts of ink is more puissant than the iron hand-held weapon.

But these examples aren't super good, I'll try and find better ones tomorrow. day after tomorrow.

T3B102

Question 1: This is an easy question. As many flowers as possible should make poison to do this.
^??? Why???

Question 2: Remember that expected value is the sum of each outcome times its probability. The expected value of a roll of a die is for instance:
1/6 * 1 + 1/6 * 2 + 1/6 * 3 + 1/6 * 4 + 1/6 * 5 + 1/6 *6 = 3.5

For each possible strategy, you have to calculate the expected number of flowers eaten, as well as the number of flowers killed by a flower to the right. You must find the probability that 1 flower will be eaten, 2 flowers will be eaten, and so on. If only ONE flower makes poison, this is fairly easy, because the probabilities will be the same for each possible outcome (as in the dice example). But if more than one flower make poison, this is much harder. To give you some numbers: if zero flowers make poison, the expected number of flowers eaten is 10 (all of them). If one makes poison, the expected number of flowers eaten is 5.5.
^... yeah no I just... I don't even know. How on EARTH did he get 5.5???

I solved this using Microsoft Excel, but you should be able to solve it without a computer.

...

But then again, I'm really bad at probability, so, you know.

T3B101

Hi. My name is Mister Kvakk. I live in a very big house in the country. Outside my house I have a lot of big gardens. In one of them I have ten beautiful, red flowers. These red flowers grow in a 5x2 rectangular shape:
FFFFF
FFFFF
The flowers had always lived in peace in this garden, until the day I allowed my dog to go into the garden. This dog has only one goal in its life: it wants to eat as many red flowers as possible.
But the flowers are not normal flowers. They can think, and are able to talk to each other. And they now need a good plan to be able to save as many flower-lives as possible.
Each of the ten red flowers has the option to develop poison. If the dog is so unlucky to eat a poisonous flower it will surely die, and thus cannot eat any more flowers. So, when the dog arrives in the garden, it will start to eat flowers in random order as long as it is alive (the dog cannot see which flowers contain poison). If none of the flowers make poison, the dog will certainly eat all of them.
But how many flowers should make poison? Unfortunately, it's not possible to save every flower. The problem is that the creation of poison is a hard task to do. When one flower develops poison, it will use all the food and water that is in the ground around it. This will kill the flower to the left (if there is a flower to the left).
The flowers are not sure about how many flowers should make poison. They think that maybe only the two flowers to the very left should do it, but they are not sure. Therefore, they need your help. 

Question 1: What is the maximum number of flowers that without risk can be guaranteed to survive?

Question 2: The flowers are risk neutral, and want to minimize the expected number of dead flowers. How many flowers should make poison to afford this?

Red roses. :) *I do not own this image, I just found it on Google Images somewhere.

...

I don't get this. Like, really, really don't get this.

T3B100

I don't get it.

Suppose there are A red marbles in the first urn, B red marbles in the second urn, C red marbles in the third urn, and D red marbles in the fourth urn. Then your probability of drawing all red marbles is A*B*C*D/625, and your probability of getting at least one blue marble is (625-A*B*C*D)/625. The king will choose whichever option is more likely. To minimize the probability of a correct prediction, you want to get these values as close as possible to each other. Equivalently, you want A*B*C*D/625 to be as close as possible to 1/2, or A*B*C*D to be as close as possible to 312.5. Since A, B, C, and D can only take on the values of 0, 1, 2, 3, 4, and 5, the possibilities are limited. The closest possible value to 312.5 is 320=5*4*4*4; none of the closer values from 306 through 319 can be achieved because each one has a prime factor greater than 5. For example, 306=2*3*3*17, 307 is a prime, 308 = 2*2*7*11, and so on. Therefore, you should place 4 red marbles and 1 blue marble in three urns, and 5 red marbles in the remaining urn. King Fischer will predict that you will get all red marbles, and you'll have a 61/125=.488 probability of drawing a blue marble and surviving.

In the end, the king takes some medicine to control his allergic reactions to much bleeding and executes you anyway. So much for all that mathematics and probability you just went through. What an anticlimax!

And this is a sad conclusion. :(

*Also, can you be allergic to bleeding? Wouldn't you have to be allergic to blood? I don't think you can be allergic to an action...