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A pair of distinct two-digit integers (n, d) is misleading if the first digit of d equals the second digit of n, and if

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A pair of distinct two-digit integers (n, d) is misleading if the first digit of d equals the second digit of n, and if you write the numbers as a fraction and "cancel" (i.e., cross out) the common digits, you get an equal fraction. For example. (16,64) is a misleading pair since 16 64 (a) Find all pairs of two-digit misleading integers. Explain how you know you have found all possible misleading two-digit pairs. (b) Are there any misleading pairs of three-digit integers? For a three-digit pair to be mis- leading, when written as a fraction. "cancelling" the first digit of d with either the second or third digit of n (where the digits being canceled are equal) results in a fraction equal in value to the original fraction. Furthermore, the two integers cannot both end in 0 (otherwise, the pair could be obtained directly from a pair of misleading two-digit num- bers).

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