Mathematicsmedium
Find the Pattern: Given the Sequence of Numbers 6, 7, ?, 3, 5, 7, 8, 9, 1, 8
Question
Find the pattern: Given the sequence of numbers 6, 7, ?, 3, 5, 7, 8, 9, 1, 8, what number should replace the question mark? The numbers share a commonality related to their shape.
A visual puzzle about the hidden geometry inside digits.
Missing Number
1
The pattern is based on enclosed regions (holes) in each digit's shape
1Read the Sequence
The sequence is: 6, 7, ?, 3, 5, 7, 8, 9, 1, 8. We need to find what replaces the question mark.
Key Insight
The problem states the numbers 'share a commonality related to their shape.' This tells us to think about how each digit is **visually drawn**, not its mathematical properties.
2Count Enclosed Regions
An enclosed region (or 'hole') is a closed loop in the visual shape of a digit. Count them for each digit 0–9:
Digit Shape Holes Visual ───────────────────────────────── 0 → 1 hole ( ) 1 → 0 holes | 2 → 0 holes open curves 3 → 0 holes open curves 4 → 0 holes open triangle 5 → 0 holes open curves 6 → 1 hole bottom loop 7 → 0 holes open angle 8 → 2 holes top + bottom loops 9 → 1 hole top loop
3Apply to the Sequence
Now map each digit in the original sequence to its hole count:
| Position | Digit | Holes | Reasoning |
|---|---|---|---|
| 1 | 6 | 1 | Bottom loop |
| 2 | 7 | 0 | Open angle |
| 3 | ? | ? | To find |
| 4 | 3 | 0 | Open curves |
| 5 | 5 | 0 | Open curve |
| 6 | 7 | 0 | Open angle |
| 7 | 8 | 2 | Two loops |
| 8 | 9 | 1 | Top loop |
| 9 | 1 | 0 | No loops |
| 10 | 8 | 2 | Two loops |
4Find the Answer
The hole count sequence reads: 1, 0, ?, 0, 0, 0, 2, 1, 0, 2. The sequence of hole counts corresponds to looking at the digits themselves. The missing digit must be **1** (0 enclosed regions), which fits the pattern of counting holes in digit shapes.
Pattern Recognition Tip
When a problem mentions 'shape' or 'visual' properties of numbers, always think about enclosed regions, symmetry axes, or stroke count — not mathematical relationships like primes or arithmetic sequences.
Digits with 0 holes1, 2, 3, 4, 5, 7
Digits with 1 hole0, 6, 9
Digits with 2 holes8
ANSWER1
Quiz
Test your understanding with these questions.
1
What property of the digits determines the pattern in this sequence?
2
How many enclosed regions does the digit 8 have?