Identifier
Values
[1] => [1] => 10 => 01 => 1
[2] => [1,1] => 110 => 011 => 2
[1,1] => [2] => 100 => 001 => 1
[3] => [2,1] => 1010 => 0101 => 2
[2,1] => [2,1] => 1010 => 0101 => 2
[1,1,1] => [3] => 1000 => 0001 => 1
[4] => [3,1] => 10010 => 01001 => 2
[3,1] => [2,2] => 1100 => 0011 => 2
[2,2] => [2,1,1] => 10110 => 01101 => 3
[2,1,1] => [3,1] => 10010 => 01001 => 2
[1,1,1,1] => [4] => 10000 => 00001 => 1
[5] => [4,1] => 100010 => 010001 => 2
[4,1] => [3,2] => 10100 => 00101 => 2
[3,2] => [2,2,1] => 11010 => 01011 => 3
[3,1,1] => [3,2] => 10100 => 00101 => 2
[2,2,1] => [3,1,1] => 100110 => 011001 => 3
[2,1,1,1] => [4,1] => 100010 => 010001 => 2
[1,1,1,1,1] => [5] => 100000 => 000001 => 1
[6] => [5,1] => 1000010 => 0100001 => 2
[5,1] => [4,2] => 100100 => 001001 => 2
[4,2] => [3,2,1] => 101010 => 010101 => 3
[4,1,1] => [3,3] => 11000 => 00011 => 2
[3,3] => [2,2,2] => 11100 => 00111 => 3
[3,2,1] => [3,2,1] => 101010 => 010101 => 3
[3,1,1,1] => [4,2] => 100100 => 001001 => 2
[2,2,2] => [3,1,1,1] => 1001110 => 0111001 => 4
[2,2,1,1] => [4,1,1] => 1000110 => 0110001 => 3
[2,1,1,1,1] => [5,1] => 1000010 => 0100001 => 2
[1,1,1,1,1,1] => [6] => 1000000 => 0000001 => 1
[7] => [6,1] => 10000010 => 01000001 => 2
[6,1] => [5,2] => 1000100 => 0010001 => 2
[5,2] => [4,2,1] => 1001010 => 0101001 => 3
[5,1,1] => [4,3] => 101000 => 000101 => 2
[4,3] => [3,2,2] => 101100 => 001101 => 3
[4,2,1] => [3,3,1] => 110010 => 010011 => 3
[4,1,1,1] => [4,3] => 101000 => 000101 => 2
[3,3,1] => [3,2,2] => 101100 => 001101 => 3
[3,2,2] => [3,2,1,1] => 1010110 => 0110101 => 4
[3,2,1,1] => [4,2,1] => 1001010 => 0101001 => 3
[3,1,1,1,1] => [5,2] => 1000100 => 0010001 => 2
[2,2,2,1] => [4,1,1,1] => 10001110 => 01110001 => 4
[2,2,1,1,1] => [5,1,1] => 10000110 => 01100001 => 3
[2,1,1,1,1,1] => [6,1] => 10000010 => 01000001 => 2
[1,1,1,1,1,1,1] => [7] => 10000000 => 00000001 => 1
[8] => [7,1] => 100000010 => 010000001 => 2
[7,1] => [6,2] => 10000100 => 00100001 => 2
[6,2] => [5,2,1] => 10001010 => 01010001 => 3
[6,1,1] => [5,3] => 1001000 => 0001001 => 2
[5,3] => [4,2,2] => 1001100 => 0011001 => 3
[5,2,1] => [4,3,1] => 1010010 => 0100101 => 3
[5,1,1,1] => [4,4] => 110000 => 000011 => 2
[4,4] => [3,3,2] => 110100 => 001011 => 3
[4,3,1] => [3,3,2] => 110100 => 001011 => 3
[4,2,2] => [3,3,1,1] => 1100110 => 0110011 => 4
[4,2,1,1] => [4,3,1] => 1010010 => 0100101 => 3
[4,1,1,1,1] => [5,3] => 1001000 => 0001001 => 2
[3,3,2] => [3,2,2,1] => 1011010 => 0101101 => 4
[3,3,1,1] => [4,2,2] => 1001100 => 0011001 => 3
[3,2,2,1] => [4,2,1,1] => 10010110 => 01101001 => 4
[3,2,1,1,1] => [5,2,1] => 10001010 => 01010001 => 3
[3,1,1,1,1,1] => [6,2] => 10000100 => 00100001 => 2
[2,2,2,2] => [4,1,1,1,1] => 100011110 => 011110001 => 5
[2,2,2,1,1] => [5,1,1,1] => 100001110 => 011100001 => 4
[2,2,1,1,1,1] => [6,1,1] => 100000110 => 011000001 => 3
[2,1,1,1,1,1,1] => [7,1] => 100000010 => 010000001 => 2
[1,1,1,1,1,1,1,1] => [8] => 100000000 => 000000001 => 1
[9] => [8,1] => 1000000010 => 0100000001 => 2
[8,1] => [7,2] => 100000100 => 001000001 => 2
[7,2] => [6,2,1] => 100001010 => 010100001 => 3
[7,1,1] => [6,3] => 10001000 => 00010001 => 2
[6,3] => [5,2,2] => 10001100 => 00110001 => 3
[6,2,1] => [5,3,1] => 10010010 => 01001001 => 3
[6,1,1,1] => [5,4] => 1010000 => 0000101 => 2
[5,4] => [4,3,2] => 1010100 => 0010101 => 3
[5,3,1] => [4,3,2] => 1010100 => 0010101 => 3
[5,2,2] => [4,3,1,1] => 10100110 => 01100101 => 4
[5,2,1,1] => [4,4,1] => 1100010 => 0100011 => 3
[5,1,1,1,1] => [5,4] => 1010000 => 0000101 => 2
[4,4,1] => [3,3,3] => 111000 => 000111 => 3
[4,3,2] => [3,3,2,1] => 1101010 => 0101011 => 4
[4,3,1,1] => [4,3,2] => 1010100 => 0010101 => 3
[4,2,2,1] => [4,3,1,1] => 10100110 => 01100101 => 4
[4,2,1,1,1] => [5,3,1] => 10010010 => 01001001 => 3
[4,1,1,1,1,1] => [6,3] => 10001000 => 00010001 => 2
[3,3,3] => [3,2,2,2] => 1011100 => 0011101 => 4
[3,3,2,1] => [4,2,2,1] => 10011010 => 01011001 => 4
[3,3,1,1,1] => [5,2,2] => 10001100 => 00110001 => 3
[3,2,2,2] => [4,2,1,1,1] => 100101110 => 011101001 => 5
[3,2,2,1,1] => [5,2,1,1] => 100010110 => 011010001 => 4
[3,2,1,1,1,1] => [6,2,1] => 100001010 => 010100001 => 3
[3,1,1,1,1,1,1] => [7,2] => 100000100 => 001000001 => 2
[2,2,2,2,1] => [5,1,1,1,1] => 1000011110 => 0111100001 => 5
[2,2,2,1,1,1] => [6,1,1,1] => 1000001110 => 0111000001 => 4
[2,2,1,1,1,1,1] => [7,1,1] => 1000000110 => 0110000001 => 3
[2,1,1,1,1,1,1,1] => [8,1] => 1000000010 => 0100000001 => 2
[1,1,1,1,1,1,1,1,1] => [9] => 1000000000 => 0000000001 => 1
[10] => [9,1] => 10000000010 => 01000000001 => 2
[9,1] => [8,2] => 1000000100 => 0010000001 => 2
[8,2] => [7,2,1] => 1000001010 => 0101000001 => 3
[8,1,1] => [7,3] => 100001000 => 000100001 => 2
[7,3] => [6,2,2] => 100001100 => 001100001 => 3
>>> Load all 385 entries. <<<
[7,2,1] => [6,3,1] => 100010010 => 010010001 => 3
[7,1,1,1] => [6,4] => 10010000 => 00001001 => 2
[6,4] => [5,3,2] => 10010100 => 00101001 => 3
[6,3,1] => [5,3,2] => 10010100 => 00101001 => 3
[6,2,2] => [5,3,1,1] => 100100110 => 011001001 => 4
[6,2,1,1] => [5,4,1] => 10100010 => 01000101 => 3
[6,1,1,1,1] => [5,5] => 1100000 => 0000011 => 2
[5,5] => [4,4,2] => 1100100 => 0010011 => 3
[5,4,1] => [4,3,3] => 1011000 => 0001101 => 3
[5,3,2] => [4,3,2,1] => 10101010 => 01010101 => 4
[5,3,1,1] => [4,4,2] => 1100100 => 0010011 => 3
[5,2,2,1] => [4,4,1,1] => 11000110 => 01100011 => 4
[5,2,1,1,1] => [5,4,1] => 10100010 => 01000101 => 3
[5,1,1,1,1,1] => [6,4] => 10010000 => 00001001 => 2
[4,4,2] => [3,3,3,1] => 1110010 => 0100111 => 4
[4,4,1,1] => [4,3,3] => 1011000 => 0001101 => 3
[4,3,3] => [3,3,2,2] => 1101100 => 0011011 => 4
[4,3,2,1] => [4,3,2,1] => 10101010 => 01010101 => 4
[4,3,1,1,1] => [5,3,2] => 10010100 => 00101001 => 3
[4,2,2,2] => [4,3,1,1,1] => 101001110 => 011100101 => 5
[4,2,2,1,1] => [5,3,1,1] => 100100110 => 011001001 => 4
[4,2,1,1,1,1] => [6,3,1] => 100010010 => 010010001 => 3
[4,1,1,1,1,1,1] => [7,3] => 100001000 => 000100001 => 2
[3,3,3,1] => [4,2,2,2] => 10011100 => 00111001 => 4
[3,3,2,2] => [4,2,2,1,1] => 100110110 => 011011001 => 5
[3,3,2,1,1] => [5,2,2,1] => 100011010 => 010110001 => 4
[3,3,1,1,1,1] => [6,2,2] => 100001100 => 001100001 => 3
[3,2,2,2,1] => [5,2,1,1,1] => 1000101110 => 0111010001 => 5
[3,2,2,1,1,1] => [6,2,1,1] => 1000010110 => 0110100001 => 4
[3,2,1,1,1,1,1] => [7,2,1] => 1000001010 => 0101000001 => 3
[3,1,1,1,1,1,1,1] => [8,2] => 1000000100 => 0010000001 => 2
[2,2,2,2,2] => [5,1,1,1,1,1] => 10000111110 => 01111100001 => 6
[2,2,2,2,1,1] => [6,1,1,1,1] => 10000011110 => 01111000001 => 5
[2,2,2,1,1,1,1] => [7,1,1,1] => 10000001110 => 01110000001 => 4
[2,2,1,1,1,1,1,1] => [8,1,1] => 10000000110 => 01100000001 => 3
[2,1,1,1,1,1,1,1,1] => [9,1] => 10000000010 => 01000000001 => 2
[1,1,1,1,1,1,1,1,1,1] => [10] => 10000000000 => 00000000001 => 1
[8,1,1,1] => [7,4] => 100010000 => 000010001 => 2
[7,4] => [6,3,2] => 100010100 => 001010001 => 3
[7,3,1] => [6,3,2] => 100010100 => 001010001 => 3
[7,2,1,1] => [6,4,1] => 100100010 => 010001001 => 3
[7,1,1,1,1] => [6,5] => 10100000 => 00000101 => 2
[6,5] => [5,4,2] => 10100100 => 00100101 => 3
[6,4,1] => [5,3,3] => 10011000 => 00011001 => 3
[6,3,2] => [5,3,2,1] => 100101010 => 010101001 => 4
[6,3,1,1] => [5,4,2] => 10100100 => 00100101 => 3
[6,2,1,1,1] => [5,5,1] => 11000010 => 01000011 => 3
[6,1,1,1,1,1] => [6,5] => 10100000 => 00000101 => 2
[5,5,1] => [4,4,3] => 1101000 => 0001011 => 3
[5,4,2] => [4,3,3,1] => 10110010 => 01001101 => 4
[5,4,1,1] => [4,4,3] => 1101000 => 0001011 => 3
[5,3,3] => [4,3,2,2] => 10101100 => 00110101 => 4
[5,3,2,1] => [4,4,2,1] => 11001010 => 01010011 => 4
[5,3,1,1,1] => [5,4,2] => 10100100 => 00100101 => 3
[5,2,1,1,1,1] => [6,4,1] => 100100010 => 010001001 => 3
[5,1,1,1,1,1,1] => [7,4] => 100010000 => 000010001 => 2
[4,4,3] => [3,3,3,2] => 1110100 => 0010111 => 4
[4,4,2,1] => [4,3,3,1] => 10110010 => 01001101 => 4
[4,4,1,1,1] => [5,3,3] => 10011000 => 00011001 => 3
[4,3,3,1] => [4,3,2,2] => 10101100 => 00110101 => 4
[4,3,2,1,1] => [5,3,2,1] => 100101010 => 010101001 => 4
[4,3,1,1,1,1] => [6,3,2] => 100010100 => 001010001 => 3
[4,2,2,2,1] => [5,3,1,1,1] => 1001001110 => 0111001001 => 5
[3,3,2,2,1] => [5,2,2,1,1] => 1000110110 => 0110110001 => 5
[2,2,2,2,2,1] => [6,1,1,1,1,1] => 100000111110 => 011111000001 => 6
[8,1,1,1,1] => [7,5] => 100100000 => 000001001 => 2
[7,5] => [6,4,2] => 100100100 => 001001001 => 3
[7,3,1,1] => [6,4,2] => 100100100 => 001001001 => 3
[7,2,1,1,1] => [6,5,1] => 101000010 => 010000101 => 3
[7,1,1,1,1,1] => [6,6] => 11000000 => 00000011 => 2
[6,6] => [5,5,2] => 11000100 => 00100011 => 3
[6,5,1] => [5,4,3] => 10101000 => 00010101 => 3
[6,4,1,1] => [5,4,3] => 10101000 => 00010101 => 3
[6,3,2,1] => [5,4,2,1] => 101001010 => 010100101 => 4
[6,3,1,1,1] => [5,5,2] => 11000100 => 00100011 => 3
[6,2,2,2] => [5,4,1,1,1] => 1010001110 => 0111000101 => 5
[6,2,1,1,1,1] => [6,5,1] => 101000010 => 010000101 => 3
[6,1,1,1,1,1,1] => [7,5] => 100100000 => 000001001 => 2
[5,5,2] => [4,4,3,1] => 11010010 => 01001011 => 4
[5,5,1,1] => [4,4,4] => 1110000 => 0000111 => 3
[5,4,3] => [4,3,3,2] => 10110100 => 00101101 => 4
[5,4,2,1] => [4,4,3,1] => 11010010 => 01001011 => 4
[5,4,1,1,1] => [5,4,3] => 10101000 => 00010101 => 3
[5,3,3,1] => [4,4,2,2] => 11001100 => 00110011 => 4
[5,3,2,1,1] => [5,4,2,1] => 101001010 => 010100101 => 4
[5,3,1,1,1,1] => [6,4,2] => 100100100 => 001001001 => 3
[5,2,2,2,1] => [5,4,1,1,1] => 1010001110 => 0111000101 => 5
[4,4,4] => [3,3,3,3] => 1111000 => 0001111 => 4
[4,4,3,1] => [4,3,3,2] => 10110100 => 00101101 => 4
[4,3,2,2,1] => [5,3,2,1,1] => 1001010110 => 0110101001 => 5
[3,3,3,2,1] => [5,2,2,2,1] => 1000111010 => 0101110001 => 5
[3,2,2,2,2,1] => [6,2,1,1,1,1] => 100001011110 => 011110100001 => 6
[10,1,1,1] => [9,4] => 10000010000 => 00001000001 => 2
[9,2,1,1] => [8,4,1] => 10000100010 => 01000100001 => 3
[8,1,1,1,1,1] => [7,6] => 101000000 => 000000101 => 2
[7,6] => [6,5,2] => 101000100 => 001000101 => 3
[7,3,1,1,1] => [6,5,2] => 101000100 => 001000101 => 3
[7,2,1,1,1,1] => [6,6,1] => 110000010 => 010000011 => 3
[7,1,1,1,1,1,1] => [7,6] => 101000000 => 000000101 => 2
[6,6,1] => [5,5,3] => 11001000 => 00010011 => 3
[6,5,2] => [5,4,3,1] => 101010010 => 010010101 => 4
[6,5,1,1] => [5,4,4] => 10110000 => 00001101 => 3
[6,4,2,1] => [5,4,3,1] => 101010010 => 010010101 => 4
[6,4,1,1,1] => [5,5,3] => 11001000 => 00010011 => 3
[6,3,2,2] => [5,4,2,1,1] => 1010010110 => 0110100101 => 5
[6,3,1,1,1,1] => [6,5,2] => 101000100 => 001000101 => 3
[5,5,3] => [4,4,3,2] => 11010100 => 00101011 => 4
[5,5,2,1] => [4,4,4,1] => 11100010 => 01000111 => 4
[5,5,1,1,1] => [5,4,4] => 10110000 => 00001101 => 3
[5,4,4] => [4,3,3,3] => 10111000 => 00011101 => 4
[5,4,3,1] => [4,4,3,2] => 11010100 => 00101011 => 4
[5,4,2,1,1] => [5,4,3,1] => 101010010 => 010010101 => 4
[5,3,2,2,1] => [5,4,2,1,1] => 1010010110 => 0110100101 => 5
[5,2,1,1,1,1,1,1] => [8,4,1] => 10000100010 => 01000100001 => 3
[5,1,1,1,1,1,1,1,1] => [9,4] => 10000010000 => 00001000001 => 2
[4,4,4,1] => [4,3,3,3] => 10111000 => 00011101 => 4
[4,4,2,2,1] => [5,3,3,1,1] => 1001100110 => 0110011001 => 5
[4,3,3,2,1] => [5,3,2,2,1] => 1001011010 => 0101101001 => 5
[4,2,2,2,2,1] => [6,3,1,1,1,1] => 100010011110 => 011110010001 => 6
[3,3,2,2,2,1] => [6,2,2,1,1,1] => 100001101110 => 011101100001 => 6
[9,5] => [8,4,2] => 10000100100 => 00100100001 => 3
[9,3,1,1] => [8,4,2] => 10000100100 => 00100100001 => 3
[9,2,1,1,1] => [8,5,1] => 10001000010 => 01000010001 => 3
[9,1,1,1,1,1] => [8,6] => 1001000000 => 0000001001 => 2
[8,3,2,1] => [7,4,2,1] => 10001001010 => 01010010001 => 4
[8,2,1,1,1,1] => [7,6,1] => 1010000010 => 0100000101 => 3
[8,1,1,1,1,1,1] => [7,7] => 110000000 => 000000011 => 2
[7,6,1] => [6,5,3] => 101001000 => 000100101 => 3
[7,5,1,1] => [6,4,4] => 100110000 => 000011001 => 3
[7,4,1,1,1] => [6,5,3] => 101001000 => 000100101 => 3
[7,2,1,1,1,1,1] => [7,6,1] => 1010000010 => 0100000101 => 3
[7,1,1,1,1,1,1,1] => [8,6] => 1001000000 => 0000001001 => 2
[6,6,2] => [5,5,3,1] => 110010010 => 010010011 => 4
[6,6,1,1] => [5,5,4] => 11010000 => 00001011 => 3
[6,5,3] => [5,4,3,2] => 101010100 => 001010101 => 4
[6,5,2,1] => [5,4,4,1] => 101100010 => 010001101 => 4
[6,5,1,1,1] => [5,5,4] => 11010000 => 00001011 => 3
[6,4,3,1] => [5,4,3,2] => 101010100 => 001010101 => 4
[6,4,2,2] => [5,4,3,1,1] => 1010100110 => 0110010101 => 5
[6,4,2,1,1] => [5,5,3,1] => 110010010 => 010010011 => 4
[6,4,1,1,1,1] => [6,5,3] => 101001000 => 000100101 => 3
[6,3,3,2] => [5,4,2,2,1] => 1010011010 => 0101100101 => 5
[6,2,1,1,1,1,1,1] => [8,5,1] => 10001000010 => 01000010001 => 3
[5,5,4] => [4,4,3,3] => 11011000 => 00011011 => 4
[5,5,3,1] => [4,4,4,2] => 11100100 => 00100111 => 4
[5,5,2,1,1] => [5,4,4,1] => 101100010 => 010001101 => 4
[5,5,1,1,1,1] => [6,4,4] => 100110000 => 000011001 => 3
[5,4,4,1] => [4,4,3,3] => 11011000 => 00011011 => 4
[5,4,3,2] => [4,4,3,2,1] => 110101010 => 010101011 => 5
[5,4,3,1,1] => [5,4,3,2] => 101010100 => 001010101 => 4
[5,4,2,2,1] => [5,4,3,1,1] => 1010100110 => 0110010101 => 5
[5,3,3,2,1] => [5,4,2,2,1] => 1010011010 => 0101100101 => 5
[5,3,2,1,1,1,1] => [7,4,2,1] => 10001001010 => 01010010001 => 4
[5,3,1,1,1,1,1,1] => [8,4,2] => 10000100100 => 00100100001 => 3
[5,2,2,2,2,1] => [6,4,1,1,1,1] => 100100011110 => 011110001001 => 6
[4,4,4,2] => [4,3,3,3,1] => 101110010 => 010011101 => 5
[4,4,3,3] => [4,3,3,2,2] => 101101100 => 001101101 => 5
[4,4,3,2,1] => [5,3,3,2,1] => 1001101010 => 0101011001 => 5
[4,3,2,2,2,1] => [6,3,2,1,1,1] => 100010101110 => 011101010001 => 6
[3,3,3,2,2,1] => [6,2,2,2,1,1] => 100001110110 => 011011100001 => 6
[9,6] => [8,5,2] => 10001000100 => 00100010001 => 3
[9,5,1] => [8,4,3] => 10000101000 => 00010100001 => 3
[9,4,1,1] => [8,4,3] => 10000101000 => 00010100001 => 3
[9,3,1,1,1] => [8,5,2] => 10001000100 => 00100010001 => 3
[9,1,1,1,1,1,1] => [8,7] => 1010000000 => 0000000101 => 2
[8,5,2] => [7,4,3,1] => 10001010010 => 01001010001 => 4
[8,4,2,1] => [7,4,3,1] => 10001010010 => 01001010001 => 4
[8,3,2,1,1] => [7,5,2,1] => 10010001010 => 01010001001 => 4
[8,2,1,1,1,1,1] => [7,7,1] => 1100000010 => 0100000011 => 3
[8,1,1,1,1,1,1,1] => [8,7] => 1010000000 => 0000000101 => 2
[7,7,1] => [6,6,3] => 110001000 => 000100011 => 3
[7,6,1,1] => [6,5,4] => 101010000 => 000010101 => 3
[7,5,1,1,1] => [6,5,4] => 101010000 => 000010101 => 3
[7,4,1,1,1,1] => [6,6,3] => 110001000 => 000100011 => 3
[7,2,2,2,2] => [6,5,1,1,1,1] => 101000011110 => 011110000101 => 6
[6,6,2,1] => [5,5,4,1] => 110100010 => 010001011 => 4
[6,6,1,1,1] => [5,5,5] => 11100000 => 00000111 => 3
[6,5,4] => [5,4,3,3] => 101011000 => 000110101 => 4
[6,5,3,1] => [5,4,4,2] => 101100100 => 001001101 => 4
[6,5,2,1,1] => [5,5,4,1] => 110100010 => 010001011 => 4
[6,5,1,1,1,1] => [6,5,4] => 101010000 => 000010101 => 3
[6,4,4,1] => [5,4,3,3] => 101011000 => 000110101 => 4
[6,4,3,2] => [5,4,3,2,1] => 1010101010 => 0101010101 => 5
[6,3,2,1,1,1,1] => [7,5,2,1] => 10010001010 => 01010001001 => 4
[6,3,1,1,1,1,1,1] => [8,5,2] => 10001000100 => 00100010001 => 3
[6,2,2,2,2,1] => [6,5,1,1,1,1] => 101000011110 => 011110000101 => 6
[5,5,5] => [4,4,4,3] => 11101000 => 00010111 => 4
[5,5,4,1] => [4,4,4,3] => 11101000 => 00010111 => 4
[5,5,3,2] => [4,4,4,2,1] => 111001010 => 010100111 => 5
[5,5,3,1,1] => [5,4,4,2] => 101100100 => 001001101 => 4
[5,4,4,2] => [4,4,3,3,1] => 110110010 => 010011011 => 5
[5,4,4,1,1] => [5,4,3,3] => 101011000 => 000110101 => 4
[5,4,3,2,1] => [5,4,3,2,1] => 1010101010 => 0101010101 => 5
[5,4,2,1,1,1,1] => [7,4,3,1] => 10001010010 => 01001010001 => 4
[5,4,1,1,1,1,1,1] => [8,4,3] => 10000101000 => 00010100001 => 3
[5,3,2,2,2,1] => [6,4,2,1,1,1] => 100100101110 => 011101001001 => 6
[4,4,4,3] => [4,3,3,3,2] => 101110100 => 001011101 => 5
[4,4,2,2,2,1] => [6,3,3,1,1,1] => 100011001110 => 011100110001 => 6
[4,3,3,2,2,1] => [6,3,2,2,1,1] => 100010110110 => 011011010001 => 6
[3,3,3,3,2,1] => [6,2,2,2,2,1] => 100001111010 => 010111100001 => 6
[9,7] => [8,6,2] => 10010000100 => 00100001001 => 3
[9,6,1] => [8,5,3] => 10001001000 => 00010010001 => 3
[9,4,1,1,1] => [8,5,3] => 10001001000 => 00010010001 => 3
[9,3,1,1,1,1] => [8,6,2] => 10010000100 => 00100001001 => 3
[8,6,2] => [7,5,3,1] => 10010010010 => 01001001001 => 4
[8,5,3] => [7,4,3,2] => 10001010100 => 00101010001 => 4
[8,4,3,1] => [7,4,3,2] => 10001010100 => 00101010001 => 4
[8,4,2,1,1] => [7,5,3,1] => 10010010010 => 01001001001 => 4
[7,7,1,1] => [6,6,4] => 110010000 => 000010011 => 3
[7,6,1,1,1] => [6,5,5] => 101100000 => 000001101 => 3
[7,5,1,1,1,1] => [6,6,4] => 110010000 => 000010011 => 3
[7,4,3,2] => [6,4,3,2,1] => 10010101010 => 01010101001 => 5
[7,3,2,2,2] => [6,5,2,1,1,1] => 101000101110 => 011101000101 => 6
[7,3,1,1,1,1,1,1] => [8,6,2] => 10010000100 => 00100001001 => 3
[6,6,3,1] => [5,5,4,2] => 110100100 => 001001011 => 4
[6,6,2,1,1] => [5,5,5,1] => 111000010 => 010000111 => 4
[6,6,1,1,1,1] => [6,5,5] => 101100000 => 000001101 => 3
[6,5,5] => [5,4,4,3] => 101101000 => 000101101 => 4
[6,5,4,1] => [5,4,4,3] => 101101000 => 000101101 => 4
[6,5,3,2] => [5,4,4,2,1] => 1011001010 => 0101001101 => 5
[6,5,3,1,1] => [5,5,4,2] => 110100100 => 001001011 => 4
[6,4,4,2] => [5,4,3,3,1] => 1010110010 => 0100110101 => 5
[6,4,3,3] => [5,4,3,2,2] => 1010101100 => 0011010101 => 5
[6,4,3,2,1] => [5,5,3,2,1] => 1100101010 => 0101010011 => 5
[6,4,2,1,1,1,1] => [7,5,3,1] => 10010010010 => 01001001001 => 4
[6,4,1,1,1,1,1,1] => [8,5,3] => 10001001000 => 00010010001 => 3
[6,3,2,2,2,1] => [6,5,2,1,1,1] => 101000101110 => 011101000101 => 6
[5,5,5,1] => [4,4,4,4] => 11110000 => 00001111 => 4
[5,5,4,2] => [4,4,4,3,1] => 111010010 => 010010111 => 5
[5,5,4,1,1] => [5,4,4,3] => 101101000 => 000101101 => 4
[5,5,3,2,1] => [5,4,4,2,1] => 1011001010 => 0101001101 => 5
[5,4,4,2,1] => [5,4,3,3,1] => 1010110010 => 0100110101 => 5
[5,4,3,3,1] => [5,4,3,2,2] => 1010101100 => 0011010101 => 5
[5,4,3,2,1,1] => [6,4,3,2,1] => 10010101010 => 01010101001 => 5
[5,4,3,1,1,1,1] => [7,4,3,2] => 10001010100 => 00101010001 => 4
[5,4,2,2,2,1] => [6,4,3,1,1,1] => 100101001110 => 011100101001 => 6
[5,3,3,2,2,1] => [6,4,2,2,1,1] => 100100110110 => 011011001001 => 6
[4,4,4,4] => [4,3,3,3,3] => 101111000 => 000111101 => 5
[4,4,3,2,2,1] => [6,3,3,2,1,1] => 100011010110 => 011010110001 => 6
[4,3,3,3,2,1] => [6,3,2,2,2,1] => 100010111010 => 010111010001 => 6
[10,1,1,1,1,1,1,1] => [9,8] => 10100000000 => 00000000101 => 2
[9,7,1] => [8,6,3] => 10010001000 => 00010001001 => 3
[9,4,1,1,1,1] => [8,6,3] => 10010001000 => 00010001001 => 3
[9,2,1,1,1,1,1,1] => [8,8,1] => 11000000010 => 01000000011 => 3
[9,1,1,1,1,1,1,1,1] => [9,8] => 10100000000 => 00000000101 => 2
[8,7,2] => [7,6,3,1] => 10100010010 => 01001000101 => 4
[8,6,3] => [7,5,3,2] => 10010010100 => 00101001001 => 4
[8,6,2,1] => [7,5,4,1] => 10010100010 => 01000101001 => 4
[8,5,2,1,1] => [7,5,4,1] => 10010100010 => 01000101001 => 4
[8,4,3,1,1] => [7,5,3,2] => 10010010100 => 00101001001 => 4
[8,4,2,1,1,1] => [7,6,3,1] => 10100010010 => 01001000101 => 4
[7,7,1,1,1] => [6,6,5] => 110100000 => 000001011 => 3
[7,6,1,1,1,1] => [6,6,5] => 110100000 => 000001011 => 3
[7,4,3,2,1] => [6,5,3,2,1] => 10100101010 => 01010100101 => 5
[7,4,2,2,2] => [6,5,3,1,1,1] => 101001001110 => 011100100101 => 6
[7,4,2,1,1,1,1] => [7,6,3,1] => 10100010010 => 01001000101 => 4
[7,4,1,1,1,1,1,1] => [8,6,3] => 10010001000 => 00010001001 => 3
[7,3,3,2,2] => [6,5,2,2,1,1] => 101000110110 => 011011000101 => 6
[6,6,5] => [5,5,4,3] => 110101000 => 000101011 => 4
[6,6,4,1] => [5,5,4,3] => 110101000 => 000101011 => 4
[6,6,3,2] => [5,5,4,2,1] => 1101001010 => 0101001011 => 5
[6,5,5,1] => [5,4,4,4] => 101110000 => 000011101 => 4
[6,5,4,2] => [5,4,4,3,1] => 1011010010 => 0100101101 => 5
[6,5,4,1,1] => [5,5,4,3] => 110101000 => 000101011 => 4
[6,5,3,3] => [5,4,4,2,2] => 1011001100 => 0011001101 => 5
[6,5,3,2,1] => [5,5,4,2,1] => 1101001010 => 0101001011 => 5
[6,5,2,1,1,1,1] => [7,5,4,1] => 10010100010 => 01000101001 => 4
[6,4,4,3] => [5,4,3,3,2] => 1010110100 => 0010110101 => 5
[6,4,4,2,1] => [5,5,3,3,1] => 1100110010 => 0100110011 => 5
[6,4,3,3,1] => [5,5,3,2,2] => 1100101100 => 0011010011 => 5
[6,4,3,2,1,1] => [6,5,3,2,1] => 10100101010 => 01010100101 => 5
[6,4,3,1,1,1,1] => [7,5,3,2] => 10010010100 => 00101001001 => 4
[6,4,2,2,2,1] => [6,5,3,1,1,1] => 101001001110 => 011100100101 => 6
[6,3,3,2,2,1] => [6,5,2,2,1,1] => 101000110110 => 011011000101 => 6
[5,5,5,2] => [4,4,4,4,1] => 111100010 => 010001111 => 5
[5,5,5,1,1] => [5,4,4,4] => 101110000 => 000011101 => 4
[5,5,4,3] => [4,4,4,3,2] => 111010100 => 001010111 => 5
[5,5,4,2,1] => [5,4,4,3,1] => 1011010010 => 0100101101 => 5
[5,5,3,3,1] => [5,4,4,2,2] => 1011001100 => 0011001101 => 5
[5,5,2,2,2,1] => [6,4,4,1,1,1] => 100110001110 => 011100011001 => 6
[5,4,4,3,1] => [5,4,3,3,2] => 1010110100 => 0010110101 => 5
[5,4,3,2,2,1] => [6,4,3,2,1,1] => 100101010110 => 011010101001 => 6
[5,3,3,3,2,1] => [6,4,2,2,2,1] => 100100111010 => 010111001001 => 6
[4,4,4,2,2,1] => [6,3,3,3,1,1] => 100011100110 => 011001110001 => 6
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Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
Map
Bulgarian solitaire
Description
A move in Bulgarian solitaire.
Remove the first column of the Ferrers diagram and insert it as a new row.
If the partition is empty, return the empty partition.
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
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reverse
Description
Return the reversal of a binary word.