Wimbles, timbles and gimbles

Logic Level 2

There are a positive number of objects in the room.

$\frac{1}{2}$ of them are wimbles.
$\frac{1}{2}$ of them are timbles.
$\frac{1}{2}$ of them are gimbles.

What is the smallest number of objects there could be in the room?

Clarification: An object can be of more than one class. For example, it could be a wimble and a timble. And an object can belong to none of the classes.

12 2 None of the other answers 10 4 14 6 8

1 solution

Geoff Pilling
Jan 5, 2017

There must be at least one object, since there are a "positive number".

Also, the number must be even, otherwise the statements saying "half of them" wouldn't make sense.

Therefore 2 is the smallest possible number if we can achieve it... So, can it be done?

Yes. If one object is a timble and the other one is a wimble and a gimble. :0)

Therefore, $\boxed2$ is the minimum number of objects.

Is $0$ a finite number? There are differing opinions: apparently physicists generally say no, mathematicians generally say yes, and real people really don't care. Anyway, in case anyone does consider $0$ to be finite, (in which case $0$ , and thus "None of the other answers", would be their choice), it might be an idea to change "finite" to "positive".

P.S.. I took note of your clarification and had one object belonging to all three categories and the other to none of them. I suppose then that there are 8 ways of achieving the answer $2$ .

Brian Charlesworth - 4 years, 5 months ago

Good point... I've clarified the question.

Geoff Pilling - 4 years, 5 months ago

Wimbles, timbles and gimbles

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