1. ## Arithmetic puzzle help

The Problem:

"The integer A consists of 666 threes, and the integer B has 666 sixes. What digits appear in the product AB?"

The (partial) Solution:

"Since 6 = 3 x 2, the product in question will be the same as that obtained by multiplying the integer A1 composed of 666 digits 9 by the integer B1 composed of 666 digits 2. etc."

Does anyone understand what this means? This is problem #72 from the USSR Olympiad Problem Book.

2. Here's the rest of the solution if it helps explain the previous sentence:

...But A1 is 1 less than 10^666; and so if B1 is multiplied by A1, the result is the same as multiplying B1 by 10^666 (which yields an integer composed of 666 digits 2 followed by 666 zeros) and subtracting the integer B1. It clearly follows that the result will be a number of form:

{22.....21} {77.....78}
__665________665__

I really dont understand what the original line means:

"Since 6 = 3 x 2, the product in question will be the same as that obtained by multiplying the integer A1 composed of 666 digits 9 by the integer B1 composed of 666 digits 2"

3. Ah I understand. They mean that 666 #9's times 666 #2's is equivalent to 666 #3's times 666 #6's. The grammar was just weird.