How many guesses would it require to correctly guess a 10 digit number?

[shivajikobardan]

TL;DR Summary

Guesses required

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.I'm trying to find how'd you calculate the number of guesses required to correctly guess a 10 digit password made up of numbers only?
Binary or decimal both ok, I just want to learn how'd you calculate it.
I think the probability is $1/3628800$

take binary case:
For guessing the first number correctly, you'd require 2 guesses.
$2^{10}$ guesses

Is this approach correct? $10^{10}$ guesses to guess 10 digit decimal number?

 

[Office_Shredder]

That looks right to me. One thing to watch out for with the wording of the problem - a regular 10 digit number can't start, since it would just be a 9 digit number at that point. But a 10 digit password certainly could.

 

[pbuk]

I think the probability is $1/3628800$

Where has this number come from?

 

[FactChecker]

Summary: Guesses required

Book link
.I'm trying to find how'd you calculate the number of guesses required to correctly guess a 10 digit password made up of numbers only?
Binary or decimal both ok, I just want to learn how'd you calculate it.
I think the probability is $1/3628800$

You lost me here. Where did this probability come from? It seems unrelated to $2^{10}$ or $10^{10}$.
Are you interested in how many are required to know that you have guessed it in every case or how many guesses would you expect it to take?

 

[Vanadium 50]

This depends on the information you get after each guess. If you get a yes/no the answer is different from higher/lower, which is different from "higher by 1234:".

In base b, the number of guesses with no other information needed to know it is $b^{10}-1$. The average is about half that.

 

[FactChecker]

This depends on the information you get after each guess. If you get a yes/no the answer is different from higher/lower, which is different from "higher by 1234:".

In base b, the number of guesses with no other information needed to know it is $b^{10}-1$. The average is about half that.

To be clear, that is to make every guess possible so that you know that one of the guesses is right. But you don't know which guess is right until you are told.