Emerging Scholars Program - Week 10

## Challenge From Last 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?

## Round and Round we go

Split up into teams of no more than 4. You will receive a slip of paper with the description of a problem to solve; do NOT share your problem with another group. You will have to use a loop to solve the problem. You will have 15 minutes to solve the problem. You will write it on the board and the rest of the class will try to guess what your original problem was. Try to use variable names that do not give the answer away (for example, use x, y, z). Be ready to lead a discussion on the time complexity of your algorithm (how many operations it does based on the input size). List of functions

## A Challenge For Next Time:

Somehow you find yourself in a room with 2 identical doors. One will lead you into an endless maze that will surely result in your death, the other will take you to freedom and happiness. You must choose one of the doors eventually because if you stay in the room, you will starve to death. In the room there are 2 identical talking birds, one always lies the other always tells the truth. You may ask only one of the birds only one simple question. This cannot be a complex sentence with lots of conjunctions. Will you ever get out of the room? If so, what question should you ask? If not, then why?