Another play with numbers website

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Discussion Overview

The discussion revolves around a number trick presented on a website, where participants explore the mathematical principles behind how the website determines a missing digit from a manipulated number. The scope includes mathematical reasoning and conceptual clarification regarding divisibility and remainders.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant describes the process of the website, which involves selecting a number, randomizing its digits, and performing subtraction to yield another number.
  • Another participant proposes that the result of the subtraction must be divisible by 9, suggesting this is key to determining the unknown digit.
  • A later reply outlines a method for deducing the missing digit based on the remainder when the number is divided by 9, providing a detailed breakdown of possible remainders and corresponding missing digits.
  • One participant raises a concern about the case when the remainder is 0, noting that it could imply two possible missing digits (0 or 9), questioning how the website resolves this ambiguity.
  • Another participant agrees with the concern and points out that the website likely prevents the selection of zero to avoid this issue.

Areas of Agreement / Disagreement

Participants express some agreement on the divisibility aspect and the method for determining the missing digit, but there is disagreement regarding the implications of a remainder of 0 and how the website handles it.

Contextual Notes

There are unresolved questions about the handling of the case when the remainder is 0 and the assumptions regarding the selection of digits, particularly the exclusion of zero.

suyver
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Another "play with numbers" website

http://digicc.com/fido/

It's probably related to the fact that we have a base-10 number system, but I fail to see how it works...

This website does the following:
1) You write down a 3 or 4 digit number, say X=x1 x2 x3 x4 (where the x's denote the digits).
2) You randomize the digits and obtain another number, say Y=x3 x2 x4 x1.
3) You subtract the largest from the smallest one. (call this one Z=z1 z2 z3 z4)
4) You select one of the digits from this number (say z3) and write the remaining numbers in any order, say z4 z1 z2 in my example.
5) Somehow, the website then tells you what the selected digit was (the z3 in my case) based only on this remaining number.

Can someone explain in some more detail what the trick is?
 
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OK, I got slightly further: My number Z=X-Y (X>Y) must be devidable by 9, right?

Is it then just the case that because the website knows that the number I imput plus the unknown digit must be dividable by 9, the value of the unknown digit can be determined? I.E.: Because it knows that the number (z4 z1 z3 UNKNOWN) is devidable by 9, and because it knows z4, z1 and z3, it can determine the value for the UNKNOWN, since z4+z1+z3+UNKNOWN must be devidable by 9?
 
OK, I think I completed the answer to my own question (great forum, this is! ;-)

This trick is that the website divides the number that I imput by 9 to see what remainder is left.
If it's 0, the missing digit had to be 9.
If it's 1, the missing digit had to be 8.
If it's 2, the missing digit had to be 7.
If it's 3, the missing digit had to be 6.
If it's 4, the missing digit had to be 5.
If it's 5, the missing digit had to be 4.
If it's 6, the missing digit had to be 3.
If it's 7, the missing digit had to be 2.
If it's 8, the missing digit had to be 1.

Is this correct?
 
There is perhaps the issu to be got round of: if the remainder is 0, then the missing digit might be 0 (it is congruent to zero mod 9 and there are two possbilities) of course there should be some reason why one of these can't happen, or there might be other reasons that allow you to decide which of these possibilites is true if both can occur
 
Good point! That must be why you are not allowed to choose a zero in the link that I gave.
 

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