asdasd (3123123) – We Solve Problems

asdasd (3123123)

Circle name: asdasd
Lesson name: 3123123
Starts at : 05.05.2020 09:00

Problems:

1.

Theory of algorithms (other) 11-13

A cat tries to catch a mouse in labyrinths A, B, and C. The cat walks first, beginning with the node marked with the letter “K”. Then the mouse $($ from the node “M”$)$ moves, then again the cat moves, etc. From any node the cat and mouse go to any adjacent node. If at some point the cat and mouse are in the same node, then the cat eats the mouse.
Can the cat catch the mouse in each of the cases A, B, C?
$\\$

$\\$
A                                                       B                                                          C

 

 

2.

Boundedness, monotonicity , Quadratic inequaities and systems of inequalities 14-17

For which natural K does the number reach its maximum value?

3.

Examples and counterexamples. Constructive proofs , Pigeonhole principle (other) , Theory of algorithms (other) 14-17

The function F is given on the whole real axis, and for each x the equality holds: F $(x + 1)$ F $(x)$ + F $(x + 1)$ + 1 = 0.
Prove that the function F can not be continuous.

4.

Dissections (other) 11-13

Two players in turn increase a natural number in such a way that at each increase the difference between the new and old values of the number is greater than zero, but less than the old value. The initial value of the number is 2. The winner is the one who can create the number 1987. Who wins with the correct strategy: the first player or his partner?

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