Find the Missing Number: The Z-Path Number Pattern Solved
Mathematical pattern puzzles and sequence brain teasers are continuous engagement drivers across social media. They test your numerical reasoning and ability to recognize progressing differences along a connected visual path.
A widely shared visual puzzle shows five red circular nodes connected in a Z-shaped line with a direct challenge:
“Find the missing number”
The nodes contain the sequence of numbers 10, 12, 16, 22, and a question mark (?).
In this guide, we trace the path step-by-step, analyze the pattern of differences between adjacent nodes, and reveal the missing number.
Deconstructing the Path: Step-by-Step Sequence Analysis
To solve the puzzle, follow the white connecting line starting from the top-left node and move through the Z-path:
[ Z-PATH NUMBER SEQUENCE ]
|
------------------------------------------------------
| | | | |
[ 10 ] [ 12 ] [ 16 ] [ 22 ] [ ? ]
• Start • Top Right • Center • Bottom Lft • Bottom Rgt
• (+2) • (+4) • (+6) • (+8) • Solution
Let’s look at the mathematical difference between each consecutive pair of connected nodes:
-
First Step (10 to 12):
$$12 – 10 = +2$$ -
Second Step (12 to 16):
$$16 – 12 = +4$$ -
Third Step (16 to 22):
$$22 – 16 = +6$$
Notice the pattern in the additions: +2, +4, +6. The amount added at each step increases by 2 (consecutive even numbers).
-
Fourth Step (22 to ?):
Following the established sequence, the next addition must be +8.
$$22 + 8 = 30$$
Pattern Progression Summary Table
| Step | From Node | To Node | Added Value | Calculation | Result |
| 1 | 10 | Top Right | +2 | $10 + 2$ | 12 |
| 2 | 12 | Center | +4 | $12 + 4$ | 16 |
| 3 | 16 | Bottom Left | +6 | $16 + 6$ | 22 |
| 4 | 22 | Bottom Right (?) | +8 | $22 + 8$ | 30 |
The Answer
The missing number represented by the question mark (?) is 30.
Why People Miscalculate
-
Assuming a Constant Difference: Solvers who look quickly often assume a fixed difference (like adding 2 or 6 repeatedly) instead of checking every step along the full path.
-
Ignoring Node Order: Trying to pair horizontal or vertical nodes independently instead of following the single continuous white line can obscure the sequence progression.
Conclusion
The correct answer to “Find the missing number” is 30. By identifying that each step increases the addition by +2 (+2, +4, +6, +8), the logic behind the puzzle becomes crystal clear!
Frequently Asked Questions (FAQ)
What is the missing number in the red circle puzzle?
The missing number is 30.
What rule governs this number sequence?
The rule is an increasing arithmetic progression of differences, where each step adds the next consecutive even integer ($+2, +4, +6, +8$).
