Batch 2 - Class 20 - Game. Kenken

Pre-Class Problems:

Bertrand paradox - Probability - Equilateral triangle in a circle. Probability of random chord has length longer than side of triangle (1) Chord rotation around one of the vertices => 1/3 (2) Make two triangles as star => 1/2 (3) Smaller circle inscribed in triangle - if mid point is outside then chord is short, else large - proportionate areas imply 1/4.
Resolution is in precise definition of "random". Homework: Do the same thing with square inside a circle - come up with three different answers

Attendance Smiti, Muskaan, Aastha, Hriday, Kushaan, Tishyaa, Anisha

Class puzzles

Ken Ken

Use this first puzzle to explain the concept

Answer: 3214, 1423, 4132, 2341
A harder puzzle

Answer: 451263, 125436, 513624, 236541, 364152,. 642315
Get kids to come up with rules of solving it - If some numbers are restricted to certain cells, other cells in same row/column must have other numbers; possibilities of addition/subtraction/multiplication/division; sum of rows/columns and properties of triangular numbers, etc.

Ultimate Tic-Tac-Toe: Lay reference of standard tic-tac-toe and its deterministic nature. Introduce the ultimate tic-tac-toe, with following rules:

Draw smaller tic-tac-toes in each square of larger tic-tac-toe
Mark a smaller square on each turn
When you get three in a row on a small board you win that small square
To win the game, win three small boards in a row
Next small board you play on is determined by which entry within previous smaller board your opponent played
If you are directed to a small board which is already full, then you get to choose which board to play on
If a small board is a tie, it neither counts as X nor O

Play online/on phone here: http://www.tictactoeten.com/

Variation where if a small board is won, even if it is not full, the player being directed there can choose which board to play on

Homework: Einstein's Puzzle: There are 5 houses in 5 different colors in a row. In each house lives a person with a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage. Other facts:

1. The Brit lives in the red house.

2. The Swede keeps dogs as pets.

3. The Dane drinks tea.

4. The green house is on the immediate left of the white house.

5. The green house's owner drinks coffee.

6. The owner who smokes Pall Mall rears birds.

7. The owner of the yellow house smokes Dunhill.

8. The owner living in the center house drinks milk.

9. The Norwegian lives in the first house.

10. The owner who smokes Blends lives next to the one who keeps cats.

11. The owner who keeps the horse lives next to the one who smokes Dunhill.

12. The owner who smokes Bluemasters drinks beer.