Find All Possible Solutions to $A$: 9 Digit Number

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Discussion Overview

The discussion revolves around finding all possible 9-digit numbers represented as $A=abcdefghi$, where each digit is unique. The number must satisfy specific divisibility conditions: the first two digits must be divisible by 2, the first three by 3, and so forth, up to all nine digits being divisible by 9. The scope includes mathematical reasoning and problem-solving.

Discussion Character

  • Exploratory, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents a potential solution, $A=123258168$, but later clarifies that all digits must be different.
  • Another participant suggests two possible solutions: $A=381654729$ and $A=801654723$, indicating that multiple solutions may exist.
  • There is confusion regarding whether participants should share their answers, as indicated by multiple posts expressing uncertainty about this guideline.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the solutions, as there are multiple proposed answers and some confusion about the conditions of the problem.

Contextual Notes

Some participants did not initially understand the requirement for all digits to be different, which may affect the validity of their proposed solutions.

Albert1
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$A=abcdefghi$ is a 9 digits number
the first 2 digits are divisible by 2
the first 3 digits are divisible by 3
---and so on
here: $ a,b,c,d,e,f,g,h,i$ are all different
please find $A$
(note :may be more than one solution)
 
Last edited:
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My solution:

381654729
did not know that i was not supposed to show my answer (Tmi)
 
Last edited:

Here's another.

[sp]
123,\!258,\!168
[/sp]
 
ineedhelpnow said:
...did not know that i was not supposed to show my answer (Tmi)

No worries! :D
 
soroban said:
Here's another.

[sp]
123,\!258,\!168
[/sp]
I am sorry,I did not make it clear
here a,b,c,d,e,f,g,h,i are all different
 
Albert said:
$A=abcdefghi$ is a 9 digits number
the first 2 digits are divisible by 2
the first 3 digits are divisible by 3
---and so on
here: $ a,b,c,d,e,f,g,h,i$ are all different
please find $A$
(note :may be more than one solution)
A=381654729, or A=801654723
 

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