# (Statistics - Easy) Superhuman Vision

Traditionally, we know that our eyes come equipped with 3 types of color photoreceptors. These 3 types allow us to see the world in all the colors we know.

In recent years, it has been discovered that some women possess a 4th color photoreceptor type, allowing them to see more colorsthan the anyone else. This is called tetrachromacy.

Now, say you are curious about how many women possess this super ability. You select a group of 150 women, have them try a test, and find the result that 6 women had this ability.

In this scenario, what is...

• the population
• the sample
• the parameter
• the statistic
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# (Logic) Blue Eyes

There is an island where all the inhabitants are perfect logicians, that is if a logical deduction can be drawn, they will do it instantly. No one new comes to the island and no one leaves. On this island no one knows the color of their own eyes. Everyone can see and keep count of everyone else's eye color at all times, but they cannot otherwise communicate.

There are 100 blue-eyed islanders, 100 brown-eyed islanders, and the guru, who happens to have green eyes. So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green). That does not tell them their own eye color; as far as they know the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and they could have red eyes.

One day the guru speaks to the islanders, but only this one time and never again. Every night afterward, a boat visits the island, and anyone who has figured out the color of their own eyes will leave the island, but the rest must stay. Standing before the islanders, without looking at anyone in particular, the guru says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?

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### Disclaimer

This is not a trick question. The answer isn't a creative leap. It is logical.

# (Math) Make a 3D Picture

This is a stereoscopic image. It can be viewed in 3D by crossing your eyes. See how

Have you ever looked at a 3D picture and wondered how it was made? I did. So I made this question.

Above is a stereoscopic image. A stereoscopic image, i.e. a stereogram, is actually 2 images of the same object taken some distance apart.  And it can be viewed in 3D simply by crossing your eyes (see how by clicking here!). This yields two pictures from slightly different angles which your brain can put together and create the illusion of depth. The question is how far apart to place them.

Your goal is to mimic the distance between your pupils, or your interpupillary distance. For 80% of pictures, the main subject will be about 6 ft away. At this distance, you would place both cameras about 2.5 inches apart, i.e. the distance between your pupils. But say you wanted to take a 3D shot of a house on a hill 50 yards away. How far apart would you have to place your cameras?

# (Logic) Mooooooooooo

QUESTION: A fast food chain recently bought a meat-processing outlet to supply it with fresh hamburgers and other meats. The shop process is: Cows enter from one end of the shop, meat gets processed in the middle, and then the meat gets packaged and delivered at the other end.

The manager of the butcher shop however cannot decide whether to have the cows walk or run into the meat processing room. How would you go about helping him figure out what to do?

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# (Physics) Setting the Pulley Trigger

The diet coke mentos funnel pours out into a 2 lbs bucket that's attached to a rope that's wrapped around a pulley. You want to figure out how much force F is initially needed to keep the bucket in a stationary state (before the coke starts pouring in).

If the coefficient of friction between the rope and the pulley is 0.15, and the pulley diameter is 6 in, what's the minimum force F?