dec 21: in lieu of math circle...

• Divide the square with two straight cuts into pieces so that each contains 2 cherries.
  
  
  
  
  
• Baby buffalo wants to go from her mom to her dad (visiting her aunt on the way. She is safe as long as she is closer to a buffalo than to any of the lions. How should she go?

• On a regular dice, the sum of dots on the opposite faces is always 7. 

 We cut the dice to get this development: can you reconstruct the dots on the left four faces?

december 7

Spent a lot of time rotating triangles.

Tried to get frogs to cross train tracks between two looooooong trains. The gap between them is long enough for a frog to get across, but how you move 1000 of them?

Tried to block a very quick cyclist from escaping: he is so fast that he rides in straight lines only. Here how one can block him with four rectangular cars:


Can you do it with three round cars?

november 9

• More work with vectors. Can we detect a right angle? 
• Coloring maps: when two colors are enough?
• Getting robots out of the maze, blindly
• Choosing socks again. Walking in square grid?

Experimenting with Hopscotch robots...

homework

1.  How many colors one needs to color this map?

2. On the left is shown what would happen to the green strip under the turn by 90 degrees around the red point. Draw what would happen if you turn by 90 degrees the yellow and the violet shapes?

3. One big bag and one small bag can hold 5 pumpkins, while two big bags and three small bags can hold 12 pumpkins. How many pumpkins each bag can hold?

november 2

• More bus stop placement: this time, interactive. Also - on a circular road...
• Robot in a labyrinth - interactive.
• Choosing socks and walking in Urbana - same thing?
• What floats, and how...

Homework

1. If the drawer contains 2 red, 2 blue, 2 green, 2 yellow and 3 pink socks, how many one needs to take (not looking), to have at least 3 different colors? 4 different colors?

2. How many colors one needs to color
this map of an island, so that no two countries of the same color had a common segment of boundary?
















3. Black robot understands all the commands: UP, DOWN, LEFT, RIGHT correctly, but the white one does the opposite (you say RIGHT, it goes LEFT etc). They listen to your commands and move simultaneously. Can you make them meet,

if they start from these positions?

or from these?

october 26

• Continue choosing the position for a bus stop. How democracy works?
• Robot in a labyrinth
• Adding vectors
• Experiment: ball in a round glass

Homework:

1. Draw three vectors:

• A at (0, 0) 
• B at (0, 5) and
• C at (3, 4).

Which is further away from A: B or C?

2. Diza has a drawer with 4 green, 4 blue and 2 red socks.  She reaches inside, not looking, and grabs some socks. How many should she get, to be sure there are at least two socks of different colors?

3. Plastic container floats in a dish, so that the water level is an inch below the rim of the dish. If you move some of the water from the dish to the container, will the water level go up? down?

october 19

homework

• Where to place a bus stop so that the total walk for the people in the village is the least?

• Can you find all ways to choose two colors out of 6?

• It is easy to get a triangular shadow out of a tetrahedron. Can you get a square shadow?

october 12

Write numbers 1...9 so that any two neighbors were at most 2 apart and 9 is in the middle.

Diza has in her box red, blue and green socks. She never puts on socks of the same color. How many ways are there for her to choose her socks? If she has B, R, G and Y?

Envelopes for the cube

Envelopes for the tetrahedron...

Midpoints of vectors...

hopscotch! making the cupcake fly. Did not do today: vectors won.

Homework

1. In a box there are 5 pencils, Red, Blue, Green, Yellow and Orange. Joan wants to choose three of them. How ways are there to choose them?

2.

Mark on graph paper three vectors:

• A(3,3);
• B(-3,1)
• C(1,-3)

Draw the midpoints between A and B, B and C, C and A.