Question:

How Many 4 Digit Numbers . . .?

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how many 4 digit numbers have the property that each of the three 2-digit numbers fromed by consecutive digits is divisible by either 19 or 31 ?

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  1. Interesting question.

    I believe the answer is seven:

    1938  (19, 93, 38)

    1957 (19, 95, 57)

    3193  (31, 19, 93)

    3195 (31, 19, 95)

    5762  (57, 76, 62)

    9319 (93, 31, 19)

    9576  (95, 57, 76)

    The two-digit multiples of 19 are 19, 38, 57, 76, and 95.

    The two-digit multiples of 31 are 31, 62, and 93.

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