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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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 seems harder than it looks initially | Comment 1 of 10
Since 10^2010 = 1 * 5^2010 * 2^2010, my initial thought was to tie an ordered list of powers of 5 that add to 2010 with an unordered list of powers of 2 that add to 2010 (unordered since the association of the power of 2 with a particular power of 5 creates different numbers). However this runs into difficulties when the list of powers of 5 includes one or more equal powers. In that case the different ordering of those two (or more) powers of 2 should not be counted, while those involved with unequal powers of 5 still must be counted.
 Posted by Charlie on 2011-03-20 12:44:51

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