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Posted on Monday, January 12th, 2009 at 6:30 pm by Universe QueenProblem 41:
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
Answer: 7652413
Implementation in Java:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 | public class Euler41 { public static boolean isPrime( int number ) { if( number < 2 ) { return false; } else if ( number == 2 ) { return true; } else { for( long i=2; i<=Math.sqrt(number); i++ ) { if( number%i == 0 ) { return false; } } } return true; } public static int factory( int n ) { int result = 1; for( int i=1; i<=n; i++ ) { result *= i; } return result; } public static int[] getPandigits( int bitLength ) { String s = String.valueOf(bitLength); for( int i=bitLength-1; i>=1; i-- ) { s += String.valueOf( i ); } String[] strings = getAllCombinations( s ); int[] numbers = new int[strings.length]; for( int i=0; i<strings.length; i++ ) { numbers[i] = Integer.valueOf( strings[i] ); } return numbers; } public static String[] getAllCombinations( String s ) { String[] combinations = new String[factory(s.length())]; if( combinations.length == 1 ) { combinations[0] = s; return combinations; } int n = factory( s.length() - 1 ); for( int i=0; i<s.length(); i++ ) { String sub; String[] subs; if( i == 0 ) { sub = s.substring( 1 ); } else if( i == s.length()-1 ) { sub = s.substring( 0, s.length()-1 ); } else { sub = s.substring( 0, i ) + s.substring( i+1 ); } subs = getAllCombinations( sub ); for( int j=0; j<subs.length; j++ ) { combinations[i*n+j] = s.charAt(i) + subs[j]; } } return combinations; } public static void main(String[] args) { int result = 0; boolean find = false; for( int i=9; i>0; i-- ) { int[] numbers = getPandigits( i ); for( int j=0; j<numbers.length; j++ ) { if( isPrime( numbers[j] ) ) { result = numbers[j]; find = true; break; } } if( find ) { break; } } System.out.println( result ); } } |
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