The heading says that even "Deep Blue" (a chess computer) won't solve this. No wonder, because the problem only looks like a chess problem, but it has nothing to do with chess.
But it's no coincidence that this is problem 16 because the given pairs are hex numbers.
Converted to decimals:
(161/163) (177/184) (229/212) (241/243) (196/?)
The sum of the numbers in each pair:
(324) (361) (441) (484) (196+?)
These are the squares of:
(18) (19) (21) (22) (?)
The missing square is 24. This means 196+? needs to be 576. This results in ?=380 which is "17C" converted to hex.
