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 Numerous Numeral Enumeration (Posted on 2011-03-20)
(A) Determine the total number of ways in which 102010(base ten) is expressible as the product of:

(I) Four distinct positive integers arranged in increasing order of magnitude.

(II) Five distinct positive integers arranged in increasing order of magnitude.

(III) Six distinct positive integers arranged in increasing order of magnitude.

(B) What are the respective answers to each of (I), (II) and (III) in part-(A), if 102010(base ten) is replaced by 102010(base 12)?

 No Solution Yet Submitted by K Sengupta Rating: 4.5000 (2 votes)

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 Solution of simple problem | Comment 6 of 10 |
10^n is expressible as the product of

(-I) Four distinct positive integers arranged in increasing order of magnitude.

in [(n+1)^2/2] ways.

There are (n+1)^2 ordered pairs of (x,y) where 10^n=2^x * 5^y
Each must be joined to one other.  Except where x and y are both n/2.

For 12^n the number is [(2n+1)(n+1)/2]

 Posted by Jer on 2011-03-21 14:12:28

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