+6 Question: What is the smallest four digit multiple of 9 with four distinct digits?
It looks easy but I don't want my solution to be found just through trial and error, is there a better and more efficient way to do this problem without just trying all multiples of nine? Thanks!! 🙏
+806
What is the smallest four digit multiple of 9 with four distinct digits?
I did a little bit of logic and a little bit of brute force.
We want the lowest four digit number. Well, it has to start with a 1. So we've got that.
What second digit would be the lowest. Obviously, 0. So we've got 10 _ _.
For the third digit, it can't be 0 or 1 so let's go with 2. Now we have 102 _.
The fourth digit can't be 0 or 1 or 2. It has to be 3 or larger.
That's the end of the logic. Now for the brute force.
Tried 1023, not evenly divisible by 9.
Tried 1024, not evenly divisible by 9.
Tried 1025, not evenly divisible by 9.
Tried 1026, Bingo. It's 114. So that's your number right there: 1026.
.
+806
What is the smallest four digit multiple of 9 with four distinct digits?
I did a little bit of logic and a little bit of brute force.
We want the lowest four digit number. Well, it has to start with a 1. So we've got that.
What second digit would be the lowest. Obviously, 0. So we've got 10 _ _.
For the third digit, it can't be 0 or 1 so let's go with 2. Now we have 102 _.
The fourth digit can't be 0 or 1 or 2. It has to be 3 or larger.
That's the end of the logic. Now for the brute force.
Tried 1023, not evenly divisible by 9.
Tried 1024, not evenly divisible by 9.
Tried 1025, not evenly divisible by 9.
Tried 1026, Bingo. It's 114. So that's your number right there: 1026.
.
+128707 Here's an approach that only uses a little trial and error
Note that 999/9 = 111
So....let's assume that our number must have the form 1 0 __ ___ where the last two digits are unique
Note that successive multiples of 9 (after 999) are
1008
1017
1026 = our number
