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 Too many threes and sixes (Posted on 2005-05-25)
The integer A consists only of 666 threes, and the integer B has only 666 sixes.

What digits appear in the product A x B ?

JUST PENCIL AND PAPER !!!

 See The Solution Submitted by pcbouhid Rating: 4.0000 (5 votes)

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 Solution Comment 10 of 10 |
For the following, a subscripted number preceding the bracketed base digit(s) will represent the occurance of the base digit(s) that number of times, e.g. 3[123] = 123123123; and || indicates the concatenation of the digits, e.g., 123 || 45 = 12345.

We are given A as 3 x 666[1] and B as 6 x 666[1].

The following pattern is a representation of the value of A x B, i.e., 3 x 6 x (n[1])2, such that n > 0 :
(n - 1)[2] || 1 || (n - 1)[7] || 8

Therefore, the digits that appear in the product A x B are:
six-hundred and sixty-five 2's, one 1,
six-hundred and sixty-five 7's, and one 8.
 Posted by Dej Mar on 2008-11-06 09:07:43

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