GeekDad Puzzle of the Week Solution – Base 2 Number Find

Last week’s previously posited puzzle:

Imagine set of 32 hexadecimal numbers, each with 8 digits. If we convert each hex digit as a four digit, base 2 number, we have a 32×32 grid of binary numbers. This is the perfect start of a number-find puzzle (like a word-find, but with numbers!)

Example: 1B8A42DE translates to 0001 1011 1000 1010 0100 0010 1101 1110.

Given the set of 32 hex numbers below, create the grid, and traverse it to find the eight 85s and the eight 170s present.

Note that standard word-grid rules apply, all numbers are 8-bit, and that binary numbers convert to decimal directionally, i.e., 00011011 and 11011000 are the same first 8 horizontal digits from different directions, but result in different base 10 numbers.

The set of 32 hex numbers that define the binary grid appear below:
1B8A42DE 8E5AB80A 59ACEE0A 36EBF6C4 31E9CCFC F4C399BA 42BC00C4 0945AE5B 35D39DFD 6185EAD9 23639B15 12011880 A542F7C1 26F5EECE F24484C1 95352420 2C252ED6 B6454713 79ACA6B0 BB5A1AC0 6F25D001 A4BB272C 7D530CB9 3A8C9EE5 E39266EA CEC721A5 A883417A CCFCCB5E 3B19B85D 7759689C 54168FEA B91C42E9

While not a trick, one simplification to the overall puzzle is that 85 and 170 are anadromes (half-palindromes) of one another when represented in binary. That is, 85 (01010101₂) and 170 (10101010₂) are simple mirror images or reversals of one another. (Interested in anadromes? See this puzzle from June!)

In any case, as the two number-find targets are anadromes of one another, only one direction of each orientation (i.e., horizontal, vertical, upper diagonal, and lower diagonal) would need to be searched; if you found an 85 in one direction, it is also a 170 in the other!

Congratulations to Justin Myers for entering a correct solution and surviving / winning the random drawing among all correct (or reasonably well-reasoned) solutions submitted. A $50 Gift Certificate from our friends at ThinkGeek should be on its way shortly!

Special thanks to Randy Slavey for providing a clear and lucid diagram of the grid, highlighting each of the targets’ positions.

Thanks to ThinkGeek for sponsoring the GeekDad Puzzle of the Week and to everyone for reading GeekDad.