Three Marbles

Logic Level 2

Each of three marbles $A,$ $B,$ and $C,$ is colored one of the three colors. One of the marbles is colored white, one is colored red, and one is colored blue. Exactly one of these statements is true:

$A$ is red.
$B$ is not blue.
$C$ is not red.

What color is marble $B?$

White Blue Red

1 solution

Jordan Cahn
Mar 13, 2019

If the first statement is true, then the third statement must also be true. Thus, the first statement is false and $A$ is not red.
Since $A$ is not red, either $B$ or $C$ must be red. If $B$ is red, then both the second and third statements would be true. Thus $C$ is the red marble.
Since $C$ is red, both the first and third statements are false, so the second statement is true. Since we already know that $C$ is the red marble, this means that $B$ must be white .

Three Marbles

1 solution

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