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Pick a number between 1 and 10

**Fred Nerd**:

I have no idea if anyone else has done this before but I decided to answer this once and for all.

You know where Marvin the Paranoid Android is demonstrating his intelligence to the mattress and asks it to pick a number between 1 and 10, and the matress says (IIRC) 7 and Marvin crushingly points out that it's wrong and how stupid the mattress is? Well I thought I'd work it out.

The answer is 2

And I'll hide the reasoning so that others have a chance to think about it and tell my why I'm wrong and why they they are smarter than Marvin.

SpoilerFirst we have to work out some rules. The fact that a robot asks it would mean it's safe to presume there is a correct answer.

Also, it's important to note that it's NOT 1 and 10 INCLUSIVE

Now, the only way there can be a correct answer is if there is only one number between 1 and 10. Which means that the question must be in a context that only allows this. The simplest context is if it is in base 3 (trinary) so the counting numbers would be 0,1,2,10,11,12,20, etc

In this case, the answer is 2.

Very simple.

**MilesAhead**:

I don't understand the reasoning bit. But do you know the riddle about 2 guards to a treasure(like an Indiana Jones riddle) .. one guard has to always answer truthfully. The other guard must always answer with a lie. You have one question to determine which is which. What is the question and which guard do you ask?

Edit: I don't remember the solution. That's why I'm asking.

**Stoic Joker**:

IIRC who you ask is irrelevant, you ask one guard what the other would say and then do the opposite. Because the liar would give the wrong answer (by nature), and the truth teller would give the liars lie.

**MilesAhead**:

IIRC who you ask is irrelevant, you ask one guard what the other would say and then do the opposite. Because the liar would give the wrong answer (by nature), and the truth teller would give the liars lie.

-Stoic Joker (February 27, 2015, 06:49 AM)

--- End quote ---

Ok, now I get it. I remembered the part about asking what the other would say. But the logic escaped me. Thanks. :)

**MilesAhead**:

@Fred. I get it now. I didn't grok the base 3 part the first time I read it. :)

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