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Greatest Root Difference (Posted on 2011-05-25) Difficulty: 3 of 5
(A) Determine the probability that for the value of a base ten positive integer M drawn at random between 11(base ten) and 10,000(base ten) inclusively, the base ten number [√M] - [3√M] is equal to the product of the digits of M.

(B) Determine the probability that for the value of a duodecimal (base 12) positive integer N drawn at random between 11(duodecimal) and 10,000(duodecimal) inclusively, the duodecimal number [√N] - [3√N] is equal to the product of the digits of N.

(C) Determine the probability that for the value of a hexadecimal (base 16) positive integer P drawn at random between 11(hexadecimal) and 10,000(hexadecimal) inclusively, the hexadecimal number [√P] - [3√P] is equal to the product of the digits of P.

Notes:

(i) None of M, N and P can contain any leading zero.

(ii) [x] denotes the greatest integer ≤ x.

No Solution Yet Submitted by K Sengupta    
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  Subject Author Date
Solutioncomputer solutionsCharlie2011-05-25 19:16:27
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