Emerging Scholars Program - Week 9

## Challenge From Last Time:

From my interview with Lawrence Livermore National Labs over this weekend:
You have a bowl with 200 fish in it. Of these fish 99% are not guppies. how many fish should you remove so that 2% of what remains are guppies? Suppose you can distinguish guppies from non-guppies.

## Warm Up

Using the ASCII character set, write ESP in binary.
Hint: The numerical equivalence of A is 65 and its binary representation is 0100 0001.

What is a "mantissa"?

1. A girl's name
2. The part of the number before the decimal point
3. The part of the number after the decimal point
4. The exponent

## Data Representation

Your task: develop an efficient way to store images. What!?! Okay, let me explain. A raw image format is stored as a large matrix with each cell defining the precise color of each corresponding pixel. Each pixel has 24 bits to store 3 values: amount of red, blue, and green. For example, storing an 8-bit number for each RGB component allows for 256 x 256 x 256 = 16,777,316 different colors (what a crayon box!). How many of those can you name? I'm not sure if sunset-orange in Cancun and sunset-orange in Puerto Vallarta count. Anyway, do you really need this much space to store an image? Does it really make a difference to the human eye if there are only 8,000,000 and not 16,000,000 colors? Well, guess what - it matters to the computer because you've just cut the memory required for storage in half! Your 20G movie just became 10G!

So, think of ways to store images that are efficient, but still retain a good amount of color information. What is a good amount? Well, that's for you to decide and then later justify to the rest of the class! From: http://www.podster.pwp.blueyonder.co.uk/misc/binary.html

## A Challenge For Next Time:

1. There are four people (a,b,c,d) behind whom a volcano is erupting. They can get to safety if they cross a bridge that's right in front of them. They have 17 minutes to cross the bridge before the lava consumes them and the bridge (they have to be completely across the bridge after 17 minutes or they fall to an unpleasant death). The bridge can only hold 2 people at a time. Also, it is dark, so they must cross the bridge with a flashlight, but they only have 1 for the whole group. Moreover, they all walk at different paces. It takes them 1, 2, 5, and 10 minutes to cross the bridge respectively, and if 2 people cross at the same time, they walk at the pace of the slower person. Can they all cross the bridge before they are fed alive to the fiery gods of the volcano? If so how? If not, why?

2. A mathematician meets another mathematician in a store. Here is their dialogue:
A: How have you been?
B: Great! Since we last talked, I've gotten married and had 3 kids
A: Really, how old are they?
B: The product of their ages is 72 and the sum of their ages is the same as the number of that building over there.
A: Right, ok... Oh wait... Hmm, I still don't know.
B: Oh sorry. The oldest one just started to play the piano.
A: That's great! My oldest is the same age

Can you tell how old mathematician B's kids are? If so, how old are they? If not, why?