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Distinct Digit Determination (Posted on 2010-10-31) Difficulty: 3 of 5
M is an 8-digit base ten positive integer of the form abcdefgh, where each of the small letters represent a different digit from 1 to 9, and N is a base ten positive real number, such that M hectares is equal to N international acres.

For a value of M drawn at random between 12345678 (base ten) and 98765432 (base ten) inclusively, determine the probability that [N] contains precisely two distinct digits.

Bonus Question:

What is the answer to the original question, if M hectares is equal to N United States survey acres?

Notes:

(i) 1 international acre is equal to 0.40468564224 hectare.

(ii) 1 United States survey acre is equal to 0.404687261 hectare.

(iii)[N] denotes the greatest integer ≤ N, and [N] cannot contain any leading zero.

No Solution Yet Submitted by K Sengupta    
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  Subject Author Date
re: computer solution -- compared to random digitsCharlie2010-10-31 14:44:13
Solutioncomputer solutionCharlie2010-10-31 14:25:51
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