Finding the Missing Digit of a 5-Digit Number

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Discussion Overview

The discussion revolves around finding a missing digit in a five-digit number derived from a process of rearranging digits and calculating the difference between two numbers. The problem involves exploring properties of numbers, specifically focusing on the digits of the resulting difference and their relationship to multiples of 9.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that the missing digit is 6, based on the reasoning that the difference must be a multiple of 9.
  • Another participant expresses confusion about why the difference must be a multiple of 9.
  • A later reply attempts to clarify this by referencing the mathematical property that (10^k - 1) is always a multiple of 9, explaining how the digits contribute to this property.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of the difference being a multiple of 9, as some express confusion about this point while others assert it as a fact.

Contextual Notes

The discussion includes assumptions about the properties of numbers and their digits, which may not be universally accepted without further clarification or proof.

BobG
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I have a five digit number - no, it's not that easy[/color]
I rearrange the digits and subtract the smaller number from the larger.

The difference is also a five digit number. I jumble up the digits of the difference. Four of the digits of the difference are 2172.

What's the missing digit of the difference?
 
Last edited:
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brute force , hapahazard hand waving and abra cadabras are giving me the missing digit as ::6[/Color]::

Let me see if i can see through some technique here ...
interesting problem btw.

-- AI
 
The missing digit would have to be 6 since the difference must be a multiple of 9.
 
duh! ofcourse!

-- AI
**i should sincerely stop playing notpron, i am losing sight of the obvious**
 
i'm missing something, why does it have to be a multiple of 9?
 
eddo said:
i'm missing something, why does it have to be a multiple of 9?

Remember (10^k - 1) is always multiple of 9.
So, for each digit A , you have:
A*10^n - A*10^m = A*(10^n - 10^m) which is multiple of 9 .
 

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