Asked by Kim
                Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5, a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11.
            
            
        Answers
                    Answered by
            drwls
            
    The answer must appear on all these lists:
498, 493, 488, 483,... 13, 8, 3.
492, 483, 474, 465,... 24, 15, 6.
492, 481, 470, 459,... 30, 19, 8.
It must end in 8 or 3 to be on the first list.
Numbers in the second list that end in 8 or 3 are:
483, 438, 393, 348, 303, 258, 213, 168, 123, 78, 33.
Numbers on the third list that end in 3 or 8 are:
448, 393, 338, 283, 228, 173, 118, 63, 8
393 is the only number on all lists.
This is rather a "brute force" method, but it works.
    
498, 493, 488, 483,... 13, 8, 3.
492, 483, 474, 465,... 24, 15, 6.
492, 481, 470, 459,... 30, 19, 8.
It must end in 8 or 3 to be on the first list.
Numbers in the second list that end in 8 or 3 are:
483, 438, 393, 348, 303, 258, 213, 168, 123, 78, 33.
Numbers on the third list that end in 3 or 8 are:
448, 393, 338, 283, 228, 173, 118, 63, 8
393 is the only number on all lists.
This is rather a "brute force" method, but it works.
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