Each number from the set $\{1,2,3,4,5,6,7,8\}$ is either colored red or blue, following these rules: a) The number $4$ is colored red, and there is at least one number colored blue. b) If two numbers $x, y$ have different colors and $x + y \leq 8$, then the number $x + y$ is colored blue. c) If two numbers $x, y$ have different colors and $x \cdot y \leq 8$, then the number $x \cdot y$ is colored red. Find all possible ways the numbers from this set can be colored.
Problem
Source: Argentina TST 2011, Problem 1
Tags: combinatorics proposed, combinatorics
22.09.2014 19:36
it's easy solution by considering variants :
05.08.2021 23:03
Blitzkrieg97 wrote: it's easy solution by considering variants :
Can this be a solution BRBRBRBR? B = blue, R = red
05.08.2021 23:04
Blitzkrieg97 wrote: it's easy solution by considering variants :
Also another quick approach is to see 1 & 3 must have same color ( since 1 + 3 = 4)
28.12.2023 16:43
AK001 wrote: Can this be a solution BRBRBRBR? B = blue, R = red Isn't it mentioned above?
24.11.2024 19:57
Blitzkrieg97 wrote: it's easy solution by considering variants :
Nótese que si 3 y 5 tienen el mismo color, en este caso azul, por la condición b, 8 debería ser rojo, la solución 3 queda descartada, también nótese que si 2 y 4 tienen el mismo color, por la condición c, 8 debería ser azul, así que la solución 2 queda descartada también