When completed, this cross-number puzzle has: a) Exactly one digit in each hexagonal box (0,1,2,3,4,5,6,7,8,or 9)
b) Only numbers that are multiples of 7 when read down and horizontally toward the left and right (BE,ADG, CF, AC, BDF, EG, AB, CDE, FG)
c) No two of those numbers are the same (you may reuse digits but not totals)
Question: What digit goes in each box and what number does ADG represent?
Note: The number that each combination of digits makes is not multiplied or added, but read as a real number. For example, if A and C are 2 and 8 respectively, the number would read 28 (which is a multiple of 7). click here for image of hexagon structure!!
I wrote a program to check every combination and got four solutions.
$$ A=4\quad A=4\quad A=4\quad A=4\\ B=2\quad B=2\quad B=9\quad B=9\\ C=9\quad C=9\quad C=2\quad C=2\\ D=3\quad D=3\quad D=3\quad D=3\\ E=1\quad E=8\quad E=1\quad E=8\\ F=8\quad F=1\quad F=8\quad F=1\\ G=4\quad G=4\quad G=4\quad G=4 $$
In every case, $ADG$ represents $434$