Checking whether a number is a Spy Number is one of the most common beginner-level Java coding interview questions.

This problem helps interviewers evaluate your understanding of:

• Loops
• Digit extraction
• Arithmetic operators
• Mathematical logic
• Problem-solving skills

Spy Number problems are commonly asked in Java, C, C++, Python, and competitive programming interviews.

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What is a Spy Number?

A Spy Number is a number whose sum of its digits is equal to the product of its digits.

In simple words,

Spy Number

=

Sum of Digits

=

Product of Digits

---

Mathematical Definition

If a number contains digits

d1

d2

d3

...

Then

Sum

=

d1 + d2 + d3 + ...

and

Product

=

d1 × d2 × d3 × ...

If

Sum = Product

then

The number is a Spy Number.

---

Example 1

Number

1124

Digits

1

1

2

4

Sum

1 + 1 + 2 + 4

=

8

Product

1 × 1 × 2 × 4

=

8

Since

8 = 8

Therefore

1124 is a Spy Number

---

Example 2

Number

123

Digits

1

2

3

Sum

1 + 2 + 3

=

6

Product

1 × 2 × 3

=

6

Therefore

123 is a Spy Number

---

Example 3

Number

1412

Digits

1

4

1

2

Sum

1 + 4 + 1 + 2

=

8

Product

1 × 4 × 1 × 2

=

8

Therefore

1412 is a Spy Number

---

Example 4

Number

145

Digits

1

4

5

Sum

1 + 4 + 5

=

10

Product

1 × 4 × 5

=

20

Since

10 ≠ 20

Therefore

145 is NOT a Spy Number

---

Some Spy Numbers

Number	Digit Sum	Digit Product	Spy Number?
1124	8	8	✅ Yes
123	6	6	✅ Yes
1412	8	8	✅ Yes
132	6	6	✅ Yes
145	10	20	❌ No
245	11	40	❌ No

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Real Interview Question

Write a Java program to check whether a given number is a Spy Number.

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Understanding the Logic

Suppose

Number = 1124

Extract every digit.

Find

• Sum of digits
• Product of digits

Finally compare

Sum == Product

If true,

the number is a Spy Number.

---

Visual Representation

Input

1124

Processing

1124

↓

Digit = 4

↓

Sum = 4

Product = 4

↓

Digit = 2

↓

Sum = 6

Product = 8

↓

Digit = 1

↓

Sum = 7

Product = 8

↓

Digit = 1

↓

Sum = 8

Product = 8

↓

Compare

↓

8 == 8

↓

Spy Number

---

Brute Force Approach

The simplest solution is

• Store the original number.
• Initialize
  • Sum = 0
  • Product = 1
• Extract one digit at a time.
• Add the digit to the sum.
• Multiply the digit with the product.
• Remove the last digit.
• Continue until the number becomes zero.
• Compare the sum and product.

---

Algorithm

Step 1

Read the number.

Step 2

Store the original number.

original = number;

Step 3

Initialize

sum = 0;

product = 1;

Step 4

Extract the last digit.

digit = number % 10;

Step 5

Update

sum += digit;

product *= digit;

Step 6

Remove the last digit.

number /= 10;

Step 7

Repeat until

number = 0

Step 8

Compare

sum == product

---

Dry Run

Input

123

Initial

sum = 0

product = 1

Digit	Sum	Product
3	3	3
2	5	6
1	6	6

Comparison

6 == 6

Output

Spy Number

---

Another Dry Run

Input

145

Initial

sum = 0

product = 1

Digit	Sum	Product
5	5	5
4	9	20
1	10	20

Comparison

10 ≠ 20

Output

Not a Spy Number

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Approach 1 — Using Iteration (Loop)

This is the simplest and most commonly asked interview solution.

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Complete Java Program

public class SpyNumber {

    public static void main(String[] args) {

        int number = 1124;

        int original = number;

        int sum = 0;

        int product = 1;

        while (number > 0) {

            int digit = number % 10;

            sum += digit;

            product *= digit;

            number /= 10;

        }

        if (sum == product) {

            System.out.println(original + " is a Spy Number");

        } else {

            System.out.println(original + " is NOT a Spy Number");

        }

    }

}

---

Output

1124 is a Spy Number

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Step-by-Step Code Explanation

Step 1

Declare the number.

int number = 1124;

Current value

1124

---

Step 2

Store the original value.

int original = number;

The original number is preserved because the variable

number

changes while extracting digits.

---

Step 3

Initialize

int sum = 0;

int product = 1;

Initially

sum = 0

product = 1

The product starts at 1 because multiplying by 0 would always result in 0.

---

Step 4

Extract the last digit.

int digit = number % 10;

For

1124

First extracted digit

4

---

Step 5

Update the sum and product.

sum += digit;

product *= digit;

Running values

Digit = 4

Sum = 4

Product = 4

---

Step 6

Remove the last digit.

number /= 10;

Values become

1124

↓

112

↓

11

↓

1

↓

0

---

Step 7

Compare

sum == product

If true,

the number is a Spy Number.

Otherwise,

it is not.

---

Example Execution

Input

Number = 132

Digits

1

3

2

Sum

1 + 3 + 2

=

6

Product

1 × 3 × 2

=

6

Output

132 is a Spy Number

---

Input

Number = 245

Digits

2

4

5

Sum

11

Product

40

Output

245 is NOT a Spy Number

---

Why Does This Work?

The algorithm extracts each digit of the number exactly once.

During each iteration:

• The digit is added to the running sum.
• The digit is multiplied into the running product.

After processing all digits, if the sum and product are equal, the number satisfies the mathematical definition of a Spy Number.

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Advantages of This Approach

• Easy to understand.
• Uses simple loops.
• Demonstrates digit extraction.
• Uses constant extra memory.
• Excellent for beginners.
• Frequently asked in coding interviews.

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Drawbacks

Although this solution is simple, interviewers often ask follow-up questions such as:

• Can you create a reusable method?
• Can you print all Spy Numbers within a range?
• What is the time complexity?
• How would you handle the number 0?
• How does a Spy Number differ from a Neon Number or Strong Number?

In Part 2, we'll cover:

• Reusable Method Approach
• Printing Spy Numbers in a Range
• Time and Space Complexity
• Comparison of Approaches
• Common Interview Mistakes
• Interview Follow-up Questions
• Related Coding Problems
• Key Takeaways
• Interview Tips

Approach 2 — Using a Reusable Method

Instead of writing the Spy Number logic inside the main() method, we can create a reusable method.

This approach improves:

• Code readability
• Reusability
• Maintainability
• Unit testing

---

Java Program

public class SpyNumberMethod {

    static boolean isSpy(int number) {

        int sum = 0;

        int product = 1;

        while (number > 0) {

            int digit = number % 10;

            sum += digit;

            product *= digit;

            number /= 10;

        }

        return sum == product;

    }

    public static void main(String[] args) {

        int number = 1124;

        if (isSpy(number)) {

            System.out.println(number + " is a Spy Number");

        } else {

            System.out.println(number + " is NOT a Spy Number");

        }

    }

}

---

Output

1124 is a Spy Number

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Approach 3 — Print Spy Numbers in a Range

Interviewers sometimes ask:

Print all Spy Numbers between 1 and N.

We can reuse the isSpy() method.

---

Java Program

public class SpyNumbersRange {

    static boolean isSpy(int number) {

        int sum = 0;

        int product = 1;

        int temp = number;

        while (temp > 0) {

            int digit = temp % 10;

            sum += digit;

            product *= digit;

            temp /= 10;

        }

        return sum == product;

    }

    public static void main(String[] args) {

        int limit = 200;

        System.out.println("Spy Numbers:");

        for (int i = 1; i <= limit; i++) {

            if (isSpy(i)) {

                System.out.print(i + " ");

            }

        }

    }

}

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Sample Output

Spy Numbers:

1 2 3 4 5 6 7 8 9 22 123 132 213 231 312 321 1124

Note: The exact output depends on the selected range.

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Dry Run (Reusable Method)

Input

Number = 123

Initial

Sum = 0

Product = 1

Processing

Digit = 3

↓

Sum = 3

Product = 3

↓

Digit = 2

↓

Sum = 5

Product = 6

↓

Digit = 1

↓

Sum = 6

Product = 6

↓

Compare

↓

6 == 6

↓

Return true

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Time Complexity

Suppose the number contains

d

digits.

---

Basic Iterative Solution

Operation	Complexity
Time	O(d)
Space	O(1)

---

Reusable Method

Operation	Complexity
Time	O(d)
Space	O(1)

---

Printing Spy Numbers in a Range

Operation	Complexity
Time	O(n × d)
Space	O(1)

where

n

is the upper limit.

---

Comparison of Approaches

Approach	Time	Space	Recommended
Loop-Based Solution	O(d)	O(1)	Good for Beginners
Reusable Method	O(d)	O(1)	✅ Best for Interviews
Range Solution	O(n × d)	O(1)	Useful Follow-up

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Common Mistakes

Mistake 1

Initializing product with 0.

Wrong

int product = 0;

Every multiplication becomes

0

Correct

int product = 1;

---

Mistake 2

Using addition instead of multiplication.

Wrong

product += digit;

Correct

product *= digit;

---

Mistake 3

Forgetting to remove the processed digit.

Wrong

while(number > 0) {

    sum += number % 10;

}

Correct

number /= 10;

Otherwise, the loop never terminates.

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Mistake 4

Comparing with the original number.

Wrong

sum == number

Correct

sum == product

The definition of a Spy Number compares sum of digits with product of digits, not with the original number.

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Mistake 5

Not using a temporary variable inside reusable methods.

Wrong

number /= 10;

If the original value is needed later, it will be lost.

Better

int temp = number;

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Interview Follow-up Questions

Q1. What is a Spy Number?

Q2. Why is 1124 a Spy Number?

Q3. Is 123 a Spy Number?

Q4. Why should the product start with 1?

Q5. Print all Spy Numbers within a range.

Q6. What is the time complexity?

Q7. Can negative numbers be Spy Numbers?

Q8. Explain digit extraction using % and /.

Q9. Compare Spy Number and Neon Number.

Q10. Write a reusable method for checking Spy Numbers.

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Related Coding Problems

• Neon Number
• Strong Number
• Armstrong Number
• Perfect Number
• Palindrome Number
• Reverse Number
• Sum of Digits
• Product of Digits
• Harshad Number

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Key Takeaways

• A Spy Number is a number whose sum of digits equals the product of digits.
• Examples include:

1

2

3

...

9

22

123

132

213

231

312

321

1124

• Extract digits using:

digit = number % 10;

• Remove digits using:

number /= 10;

• Initialize:

sum = 0;

product = 1;

• Compare:

sum == product

• The solution runs in O(d) time and O(1) extra space, where d is the number of digits.

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Frequently Asked Interview Questions

Q1. What is a Spy Number?

A Spy Number is a number whose sum of digits is equal to the product of digits.

Example

123

Sum = 1 + 2 + 3 = 6

Product = 1 × 2 × 3 = 6

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Q2. Why is 22 a Spy Number?

Digits

2

2

Sum

2 + 2 = 4

Product

2 × 2 = 4

Since

4 = 4

it is a Spy Number.

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Q3. Are all single-digit numbers Spy Numbers?

Yes.

For any single-digit number d:

Sum = d

Product = d

Therefore, every single-digit number from 1 to 9 is a Spy Number.

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Q4. Can a number containing zero be a Spy Number?

Usually No, because the product becomes 0 whenever any digit is 0.

Example

120

Sum = 3

Product = 0

However, always verify by calculating both values.

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Q5. What is the difference between a Spy Number and a Neon Number?

Spy Number	Neon Number
Sum of digits = Product of digits	Sum of digits of the square = Original number
Example: 123	Example: 9

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Interview Tip

If an interviewer asks:

"Write a Java program to check whether a number is a Spy Number."

Start by explaining the mathematical definition:

A Spy Number is a number whose sum of digits equals the product of digits.

Implement the loop-based solution using % to extract digits and / to remove them. Maintain two variables—sum initialized to 0 and product initialized to 1. Explain why the product must start with 1 instead of 0, as initializing it to 0 would make every multiplication result in 0. Mention that the algorithm runs in O(d) time with O(1) extra space, where d is the number of digits. Finally, show how the logic can be moved into a reusable isSpy() method and extended to print all Spy Numbers within a specified range.