Circle Second (Lesson2) – We Solve Problems

#### Circle Second (Lesson2)

Circle name: Circle Second
Lesson name: Lesson2
Starts at : 14.05.2020 10:00

Problems:

#### Game theory (other) , Odd and even numbers11-13

Petya and Misha play such a game. Petya takes in each hand a coin: one – 10 pence, and the other – 15. After that, the contents of the left hand are multiplied by 4, 10, 12 or 26, and the contents of the right hand – by 7, 13, 21 or 35. Then Petya adds the two results and tells Misha the result. Can Misha, knowing this result, determine which hand – the right or left – contains the 10 pence coin?

#### Examples and counterexamples. Constructive proofs , Pigeonhole principle (other)13-15

What is the maximum number of kings, that cannot capture each other, which can be placed on a chessboard of size $8 \times 8$ cells?

#### Puzzles12-13

Rebus. Solve the numerical rebus AAAA-BBB + SS-K = 1234 $($different letters correspond to different numbers, but the same letters each time correspond to the same numbers$)$

#### Puzzles13-14

Can the equality $K \times O \times T$ = $U \times W \times E \times H \times S \times L$ be true if instead of the letters in it we substitute integers from 1 to 9 $($different letters correspond to different numbers$)$?

#### Puzzles12-13

Solve the rebus $AC \times CC \times K$ = 2002 $($different letters correspond to different integers and vice versa $)$.

#### Mathematical logic (other)12-13

We are looking for the correct statement. In a notebook one hundred statements are written:

1$)$ There is exactly one false statement in this notebook.

2$)$ There are exactly two false statements in this notebook.

100$)$ There are exactly one hundred false statements in this notebook.

Which of these statements is true, if it is known that only one is true?

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