Consider all 6 - digit numbers of the form where is odd. Determine the number of all such 6 - digit numbers that are divisible by 7.
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a b c c b a is divisible by 7, so a b c − c b a is divisible by 7, and also a − c is divisible by 7.
b has 5 possibilities, 1 , 3 , 5 , 7 , 9
( a , c ) has 1 4 possibilities, a = c has 9 possibilities, a − c = 7 has 3 possibilities, c − a = 7 has 2 possibities.
Hence 5 × 1 4 = 7 0