Solving a Math Problem: Number Interchange & 9 More

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Discussion Overview

The discussion revolves around a mathematical problem involving a two-digit number where the digits are interchanged, resulting in a number that is 9 more than the original. Participants explore the implications of the conditions given, particularly focusing on the relationship between the digits.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant sets up equations based on the problem statement, concluding that both equations derived are the same, leading to a question about whether there is enough information to find a unique solution.
  • Another participant asserts that the problem is underdetermined, indicating that any number where the second digit is one more than the first digit satisfies the conditions.
  • A different participant emphasizes that it is not possible to find unique values, suggesting that the digits can be represented as x and 1+x, with x constrained between 0 and 9.
  • Another participant challenges the initial claim of finding the number 12, suggesting that other numbers such as 23, 34, 45, 56, 67, and 89 also meet the problem's criteria, reinforcing the idea that multiple solutions exist.

Areas of Agreement / Disagreement

Participants generally agree that the problem does not yield a unique solution, with multiple numbers satisfying the conditions. However, there is some contention regarding the interpretation of the initial findings and the implications of the equations derived.

Contextual Notes

The discussion highlights the dependence on the definitions of the digits and the constraints imposed by the problem, which leads to multiple valid solutions without resolving the uniqueness of the answer.

vepore2
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Let us consider a two digit number. If the digits are interchanged, the new number is 9 more than the original number. The second digit of the original number is one more than the first digit. Find the number.
Let x be the first digit and y be the second digit

(10y + x) - (10x +y) = 9
and
y -x =1

(10y + x) - (10x +y) = 9
9y -9x = 9
y - x = 1

I find out that both equations are the same does that mean that there isn't enough information or have I done something wrong?
From messing around I find the number is 12
 
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It is underdetermined. Any number where y-x = 1 will work.
 
U can't find two separate value OR unique Values

Generally the digits will be x at units place and 1+x at ten's digit and 0<x<9
 
What do you mean "From messing around I find the number is 12"? Just how messy were you? Did you think about 23? 34? 45? 56? 67? 89? All those number have exactly the properties you require. (Of course, that is exactly what Moose352 said: "Any number where y-x = 1 will work."
 

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