Pinocchio problem

Logic Level 1

One day Pinocchio said, " My nose will grow now ". What will be the out come of this event.

Info: Pinocchio is a creature that looks like a small boy made out of wood, the main property of this creature is that its nose will grow every time it lies.

Nose will grow by half Nose will grow Its a paradox, we cant say weather the nose will grow or not. Nose will not grow

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1 solution

Let us consider what will happen when he tells the truth.

If Pinnochio is telling the truth by saying,"My nose will grow now" then his nose would not grow (as it only grows when he's telling a lie) But by his statement,his nose should grow (as he is telling the truth).Contradiction.

Now let us consider what will happen if Pinnochio is telling a lie.

If Pinnochio is lying by saying,"My nose will grow now." then his nose should grow (as he is telling a lie).But if he's lying by stating,"My nose will grow now" and it actually grows in size,then he's telling the truth.But we assumed beforehand that he is lying.Contradiction.

Since both the cases of Pinnochio telling a lie or the truth lead to contradictions,hence the answer is that It’s a paradox \boxed{\text{It's a paradox}}

It is similar to this:

This statement is false.

Is the above statement true or false?

Nihar Mahajan - 5 years, 2 months ago

Usually this is consider a paradox, but if you take into account the word "now" then the answer could be different.

Let's consider "now" be the time frame about 1 second since spoken. Assume Pinocchio say the statement at 9:00:00 AM, then if his nose does not grow at 9:00:01 AM then his statement is false, thus is nose could grow after that.

Tran Hieu - 5 years, 2 months ago

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