for D, 10.20

1/3+1/6=
1/3-1/6=
2/3+1/6=
1/2+1/4+1/8=
1/2+1/4+1/8+1/16=

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A, B and C are looking at a green breeble (a magical creature).

A: B says the breeble has three legs!
B: No, it has five thousand legs.
C: Just one of you is lying.

Indeed, just one of A, B and C is lying. Who?

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What is bigger:
9*9 or 99?
9*9*9 or 999?
5/2 or 7/3?
555/2 or 777/3?

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10x+2y=9
10x-y=0.

3x+y=0
2x-4y=0.

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September 25, 2016 - Math Circle 2.0

Warm-up

In a certain flower garden, each flower was either red, yellow, or blue.  All three colors were in the garden.  One person visited and said that whatever 3 flowers you picked, one was going to be yellow. Another person visited and said that whatever 3 flowers you picked, one was going to be red.  Is it true that for every 3 flowers you pick, one will be blue as well?  Why?

Fibonacci numbers 

We write all possible sequences of black and white dots, such that no two black next to each other. How many different sequences are there?

2  of length 1 of them; 

3 of length 2; 

5 of length 3... 

Writing them one under another - if longer sequence extends the shorter one - helps.

The students extended this picture and found that there were 8 sequences of length 3.

Battleship

The kids formed two teams of two and used coordinates to find each others' hidden battleships.