Input a number to check if it is a Vampire Number or enter a start and end range to generate all Vampire Numbers within that range.
A Vampire Number is a special number formed by rearranging the digits of two factors (known as fangs), which are equal-length integers. Specifically, a Vampire Number \(N\) satisfies the following properties: \( N = x \times y \) Where:
To determine if a number \(N\) is a Vampire Number:
Solution:
1. Digit count check:
1023 has 4 digits, so it may be a Vampire Number.
2. Find factor pairs:
Possible factor pairs with equal digit counts:
\(11 \times 93 = 1023\)
\(31 \times 33 = 1023\)
3. Compare digit combinations:
For \(11\) and \(93\): The digits are \(1, 1, 9, 3\), but \(1023\) has digits \(1, 0, 2, 3\). No match.
For \(31\) and \(33\): The digits are \(3, 1, 3, 3\), but \(1023\) has digits \(1, 0, 2, 3\). No match.
Result: 1023 is not a Vampire Number.
Solution:
1. Digit count check:
1260 has 4 digits, so it may be a Vampire Number.
2. Find factor pairs:
Possible factor pairs:
\(14 \times 90 = 1260\)
\(15 \times 84 = 1260\)
\(18 \times 70 = 1260\)
\(20 \times 63 = 1260\)
\(21 \times 60 = 1260\)
\(28 \times 45 = 1260\)
\(30 \times 42 = 1260\)
\(35 \times 36 = 1260\)
3. Compare digit combinations:
The digits of \(21\) and \(60\) (\(2, 1, 6, 0\)) match perfectly with the digits of \(1260\).
Result: 1260 is a Vampire Number.
Solution:
1. Digit count check:
126000 has 6 digits, so it may be a Vampire Number.
2. Find factor pairs:
Possible factor pairs include:
(144, 875), (168, 750), (175, 720), (225, 560), (240, 525), (250, 504), (252, 500), (315, 400), (336, 375), (375, 336), (400, 315), (500, 252), (504, 250), (525, 240), (560, 225), (720, 175), (750, 168), (875, 144)
3. Compare digit combinations:
None of these factor pairs match the digit combination \(1, 2, 6, 0, 0, 0\).
ResultResult