Asked by Denny
                A positive whole number is called stable, if at least one of its digits has the same value as its position in the number. Example, 78247 is stable because a 4 appears in the 4th position. How many stable 3-digit numbers are there?
            
            
        Answers
                    Answered by
            oobleck
            
    the number must have the form
xx3 or x2x or 1xx
Since there are no leading zeroes, that leaves
9*10 + 9*10 + 10*10 possibilities
    
xx3 or x2x or 1xx
Since there are no leading zeroes, that leaves
9*10 + 9*10 + 10*10 possibilities
                    Answered by
            ak
            
    Answer is 252.
You should not double count numbers.
    
You should not double count numbers.
                    Answered by
            Yeet
            
    Yeet a yeet
    
                    Answered by
            Yeet 2.0
            
    Yeet a yeet 2.0
    
                    Answered by
            Yeet 3.0
            
    Yeet a yeet 3.0
    
                    Answered by
            doomah
            
    350?
    
                    Answered by
            Anominous
            
    530
    
                    Answer
            
    260
    
                    Answer
            
    hi
    
                    Answered by
            GPT 3.5
            
    The correct answer is indeed 260. We can break down the possibilities as follows:
For numbers in the form "xx3", the first digit can be any number from 1 to 9, and the second digit can be any number from 0 to 9, except for 3. So there are 9 * 10 = 90 possibilities for this case.
For numbers in the form "x2x", the first digit can be any number from 1 to 9, and the third digit can also be any number from 1 to 9. So there are 9 * 9 = 81 possibilities for this case.
For numbers in the form "1xx", the second digit can be any number from 0 to 9, except for 1. So there are 9 * 10 = 90 possibilities for this case.
Therefore, the total number of stable 3-digit numbers is 90 + 81 + 90 = 261.
Apologies for the initial incorrect response.
    
For numbers in the form "xx3", the first digit can be any number from 1 to 9, and the second digit can be any number from 0 to 9, except for 3. So there are 9 * 10 = 90 possibilities for this case.
For numbers in the form "x2x", the first digit can be any number from 1 to 9, and the third digit can also be any number from 1 to 9. So there are 9 * 9 = 81 possibilities for this case.
For numbers in the form "1xx", the second digit can be any number from 0 to 9, except for 1. So there are 9 * 10 = 90 possibilities for this case.
Therefore, the total number of stable 3-digit numbers is 90 + 81 + 90 = 261.
Apologies for the initial incorrect response.
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