Vampire Number — Definition, Formula & Examples
A vampire number is a number with an even number of digits that can be split into two smaller numbers (called "fangs") whose digits are a rearrangement of the original number's digits, and whose product equals the original number.
A vampire number is a composite integer with digits such that , where and (the fangs) each have exactly digits, the digits of and together form a permutation of the digits of , and at most one of , has a trailing zero.
How It Works
To check whether a number is a vampire number, first confirm it has an even number of digits. Then try to find two factors, each with half as many digits, whose digits together are exactly the same multiset as the original number's digits. Both fangs cannot end in zero. The smallest vampire numbers all have four digits, and the first one is .
Worked Example
Problem: Verify that 1395 is a vampire number.
Step 1: Count the digits. 1395 has 4 digits, which is even, so each fang must have 2 digits.
Step 2: Search for two 2-digit factors of 1395. Testing: 15 × 93 = 1395.
Step 3: Check the digits. The fangs 15 and 93 use the digits {1, 5, 9, 3}. The original number 1395 has the digits {1, 3, 9, 5}. These are the same set, so the condition is satisfied.
Answer: 1395 is a vampire number with fangs 15 and 93.
Why It Matters
Vampire numbers are a gateway into recreational number theory — the art of playing with numbers to discover surprising patterns. Searching for them builds skills in factoring, digit manipulation, and systematic problem-solving that apply directly in algebra and computer science.
Common Mistakes
Mistake: Accepting a factorization where both fangs end in zero, like treating 126000 = 210 × 600 as valid.
Correction: The definition requires that at most one fang ends in zero. If both fangs have trailing zeros, the pair is disqualified.