VTMO 2020 — Grade 8 — vtmo Question 13

Natural numbers $a , b , c$ satisfy exactly one true statement per pair: $X$ a $^{2} + b^{2} + c^{2} = 165$ or $bc = 28$; $Y c \gt b$ or $9$ divides $b + c$; $Z = 8$ divides $c$ or $c = 4$. Find $a + 2 b + 3 c$.