CISRA Puzzle Competition 2008 - Solutions
This is the archive of the 2008 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.
D.2 String Theory
One way to begin is to notice that the first five digits of each line represent the numbers 1 to 8 in binary - with one missing, namely the number 5. Arranging them in ascending order gives you:
1: 00001011100011001001111101.....00000 2: 000100101000111110.....0111011000001 3: 0001101100111010100100.....111110001 4: 001001101010000011101.....1111100010 5: ? 6: 00110100111.....01010111110010000011 7: 00111011010111110001001010000.....11 8: 01000110110.....01011100100111110100
One line is left over, because its first five digits are missing:
?: .....0111010011011000001000111110010
You might guess that this line is the one missing from the sequence above. That would mean that its missing digits are the binary representation of 5, or 00101:
001010111010011011000001000111110010
A careful examination of this completed line shows that every possible sequence of five digits appears in it exactly once.
001010111010011011000001000111110010 001010111010011011000001000111110010 001010111010011011000001000111110010 001010111010011011000001000111110010 etc... 001010111010011011000001000111110010 001010111010011011000001000111110010 001010111010011011000001000111110010 001010111010011011000001000111110010
Such a string of characters is a shortest common superstring of all possible five-digit binary strings. For each of the remaining lines, there's only one way to insert the missing digits to give them the same property. The completed sequences, arranged in ascending order as shown above, are:
000010111000110010011111011010100000 000100101000111110011010111011000001 000110110011101010010000010111110001 001001101010000011101100101111100010 001010111010011011000001000111110010 001101001110110001010111110010000011 001110110101111100010010100000110011 010001101100000101011100100111110100
In binary, the filled-in sections represent, respectively, the numbers 21, 13, 2, 18, 5, 12, 12, and 1. Being numbers between 1 and 26, you can convert these to letters of the alphabet, which gives you the answer: UMBRELLA.
It's also possible to fill the gaps without re-ordering the lines first. This leads to the string of letters "lmeaublr", which can then be anagrammed to UMBRELLA.