- We started with yet another weighing problem: one has 4 coins that look identical, but two of them are heavier than the other couple. How many weighings on a scale we need to detect, which two are heavier?
Answer: 2 weighings is enough.
- We added numbers: CXC+XIX=?
- The game of Nim is simple: two players take in turn from a pile one or two tokens from the top. Whoever takes the bottom token, wins.
We established that in piles of size 1 or 2, the first player wins, in the pie of 3, the second player does - provided they make the best possible moves...
- Lastly, we played an unusual game: one had to choose (secretly) one of eight objects, and the voters for the most popular one would be the winners.
Then we changed the rules: the voters for the least popular would be the winners.
Then - the voters for the object getting exactly 2 votes...
Homework:
- Now, you have 3 coins, all of different weights. How many weighings you need to find the heaviest, the lightest coins?
- In the game of Nim, who wins if there are 6 tokens in the pile?
- Add CXL+XXXVII+XXIII=?
- Several games:
- On a city map, take a point: if you meet most of your friends, you win.
- Think of a number (1-9) - those with most claimed number, win.
- Those with least claimed number win.
- Sharing stuff: Pete and Claire have 2 and 4 cups of rice. They cook together a wok of delicious fried rice.
- A stranger comes to them, and buys a third f their rice, paying $5. How they have to share the money?
- What if they had in the beginning 2 and 3 cups - how they should split the money now?
- We will do vectors (from the homework and like)
- Roman numerals, again! what is XC + XXIV?
- We'll continue statistical estimation experiments...
Homework:
- Recall, that if you have 9 lookalike coins, one of which is fake (heavier), you can find it with just 2 weighing on the scale (remember how?).
Can you do the same with 10 coins? Can you find the fake coin among 10 coins with 3 weighings? among 11 coins with 3 weighings? 20? 25? How?
- If you lost you friend in Paris (and neither of you have a cell phone!), how you would look for her?
- If you have vectors A(1,2), B(-2,1) and C(1,-3), what is A+B+C? (Recall, that you have to walk these three vectors one after another, starting at (0,0)).
