Emerging Scholars Program - Week 13

## A Challenge From Last Time:

A group of people live on an island. They are all perfect logicians. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. If anyone has figured out the color of their own eyes, they [must] leave the island that midnight. On this island live 100 blue-eyed people, 100 brown-eyed people, and the Guru. The Guru has green eyes, and does not know her own eye color either. Everyone on the island knows the rules (but are not given the total numbers) and is constantly aware of everyone else's eye color. Everyone keeps a constant count of the total number they see of each (excluding themselves). However, they cannot otherwise communicate. So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes, but that does not tell them their own eye color; it could be 101 brown and 99 blue. Or 100 brown, 99 blue, and the one could have red eyes.

The Guru speaks only once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone with blue eyes."

Who leaves the island, and on what night?

## Parallel Computing

Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain results faster. The idea is based on the fact that the process of solving a problem usually can be divided into smaller tasks, which may be carried out simultaneously with some coordination.     - Wikipedia

### Group activity I ~ 10 minutes

Ever wished you had 4 arms or maybe 4 eyes so you could watch TV and play a computer game at the same time? Assume you can (at your wish) split into 4 people in order to accomplish some kind of task(s). Think of 7 activities for which it would be useful to have this kind of ability. Present to the class.

Minor comment by me

### Group activity II ~ 10 minutes

Think of 7 things you can't do better/faster if you had the splitting-into-four-people ability. Are any of the things you mentioned previously not possible? Present to class.

### Some computers have A LOT of processors

• Most computers have hyperthreading - pretty much means 2 CPUs
• Most servers have 2,4,8,16 processors
• Clusters
• SETI at home / BOINC
• Deep Blue vs Garry Kasparov
• Blue Gene ~280 teraflops (1012 FLOPS)

## A Challenge For Next Time:

• An Arab sheik is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?

• This one is tricky, be careful You have a bag of 50 blue balls (call this bag B) and a bag of 50 red balls (call this bag R). Little mischievous Bobby comes by and mixes the two bags by doing the following: He first grabs a handful of balls from the R bag and throws them into the Bbag. Next, he grabs a handful of the balls from the B bag and throws them into the R bag. He does this 3 times, then giggles and runs away. When you come back, which of your bags is more "pure" - that is, which bag contains a higher concentration of balls of its original color? Be careful, I messed this up the first time I solved it