In complex geometric number puzzles, try to group elements into symmetrical subsets (like the two triangles here). Often, a property like "Sum(Inner) - Sum(Outer) = Constant" holds true for all subsets.
Step 1: Understanding the Concept:
This numerical reasoning puzzle involves finding a mathematical relationship between numbers placed in different segments of a geometric figure. Step 2: Detailed Explanation:
Let's analyze the groups of numbers. The star is formed by two overlapping large triangles.
Group 1 (Small points): The outer vertices are 1, 5, 3. The inner cells next to them are 2, 6, 4.
Pattern for Group 1: Inner Number = Vertex $+ 1$.
Check: $1 + 1 = 2$; $5 + 1 = 6$; $3 + 1 = 4$. Total inner sum = $2 + 6 + 4 = 12$.
Group 2 (Large points): The outer vertices are 15, 17, 19. The inner cells next to them are ?, 16, 18.
Let's check the sum logic: In Group 1, sum of inner numbers ($12$) is 3 more than the sum of outer vertices ($1+5+3 = 9$).
In Group 2, the sum of outer vertices is $15 + 17 + 19 = 51$.
Following the same logic, the sum of inner numbers should be $51 + 3 = 54$.
Sum of inner numbers in Group 2 = $? + 16 + 18 = 54$.
$? + 34 = 54 \Rightarrow ? = 54 - 34 = 20$. Step 3: Final Answer:
The missing number is 20.
