Each answer consists of a two-word phrase with a six-letter first word and a shorter second word. Each letter from the second words is taken from the letters that spell either “BLACK” or “WHITE.” That, coupled with the six-letter first words (and the word “mastermind” in the story text), suggests a game of Mastermind to determine a six-letter answer, with the second word in each puzzle answer representing the responses to the guess. (A black peg represents a correct letter in the answer appearing in the correct position; a white peg represents a correct letter in the wrong position.)

• ANGKOR: WAT = 1 black, 2 white
• KHAGAN: BEK = 2 black, 1 white
• LEAVES: BE = 1 black, 1 white
• MORGAN: HILL = 2 black, 2 white
• PACKED: ICE = 1 black, 2 white
• PAMPAS: CAT = 2 black, 1 white
• PAVING: TILE = 1 black, 3 white
• PIGEON: LAKE = 3 black, 1 white
• RAPIER: WIT = 0 black, 3 white
• TAMPER: WITH = 0 black, 4 white

The only six-letter string satisfying all of these clues is PEGMAN, the stick-figure mascot for Google Maps, who will be happy to help our heroes find their way through the city.