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 !!!

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