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

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The discussion focuses on finding a 9-digit number $A=abcdefghi$ where each digit is unique. The number must meet specific divisibility criteria: the first two digits are divisible by 2, the first three by 3, and so forth. Participants share potential solutions, including 381654729 and 801654723, while clarifying the requirement for distinct digits. The conversation highlights the challenge of adhering to the rules while generating valid numbers. Multiple solutions are acknowledged as possible.
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
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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