Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with 4-digit number in which each of two digits appears two times.

“Look, daddy!” she exclaims. “That number is evenly divisible by the age of each of us kids!”

“That’s right,” replies Mr. Jones, “and the last two digits just happen to be my age.”

What is the four digit number in the license plate?

Source: 2006 AMC 10/12B #25 (American Mathematics Contest)

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Nice! I managed to solve the problem without using the fact that the last two digits equal the age of Mr Jones, but that involved looking through many cases. I searched and found a much faster solution using that clue.

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Cute puzzle! However, tpc, the answer is not unique if you don’t have the fact that the last two digits equal the age of Mr. Jones. I guess a follow up question would be “What other answer(s) would be possible without that constraint?”

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Oops – didn’t realize that the answer was already posted.

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Dave,

As far as I remember, I don’t think there are other answers, for example 9900 is neither divisible by 8 nor 7, so we didn’t need to discard that based on Mr Jones’ age, although that would be much faster.

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