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

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• shivajikobardan
In summary, the conversation discusses the number of guesses required to correctly guess a 10 digit password made up of numbers only. It mentions the use of binary and decimal, and the probability of 1/3628800. The correct approach for calculating the number of guesses is also mentioned, taking into account the information received after each guess. The final summary mentions the formula for the number of guesses and clarifies that it is to make every guess possible, but the correct guess is not known until told.
shivajikobardan
TL;DR Summary
Guesses required
.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?

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.

shivajikobardan said:
I think the probability is ## 1/3628800 ##
Where has this number come from?

shivajikobardan said:
Summary: Guesses required

.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?

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.

## 1. How many guesses would it take to correctly guess a 10 digit number if there are no restrictions on the numbers used?

The number of guesses required would be 10 billion (10^10) as there are 10 digits and each digit can be any number from 0-9.

## 2. How many guesses would it take to correctly guess a 10 digit number if the numbers used can only be from 0-5?

The number of guesses required would be 9,765,625 (5^10) as each digit can only be 0-5.

## 3. Is there a way to reduce the number of guesses needed to correctly guess a 10 digit number?

Yes, if there are certain patterns or rules in the number, it is possible to reduce the number of guesses needed. For example, if the number is a date (MMDDYYYY), the number of guesses needed would be 365 (assuming it is a valid date).

## 4. How does the length of the number affect the number of guesses needed?

The number of guesses needed increases exponentially with the length of the number. For example, a 20 digit number would require 100 trillion (10^20) guesses, which is significantly more than a 10 digit number.

## 5. Can a computer algorithm be used to accurately guess a 10 digit number?

Yes, a computer algorithm can be used to systematically guess a 10 digit number. However, the time and number of computations required would depend on the complexity of the algorithm and the number of restrictions on the numbers used.

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