Danish director Morten Tyldum (Headhunters) and screenwriter Graham Moore have set at the center of this remarkable World War II period film several puzzles. One relates to the German’s Enigma device, which every day generated the codes the Nazis used to relay messages and orders to military forces. The British war department had found the code formidable but were determined to give a team of mathematicians and logicians led by the human conundrum Alan Turing (Benedict Cumberbatch) a chance to break it. And therein lies the second puzzlement: what could Turing — an inapproachable and mercilessly disapproving cuss — have possibly told Prime Minister Winston Churchill to convince him to hand over more than 100,000 pounds so that Turing could build a decoding machine that no one except Turing was sure would work. The audience is never told directly, although the answer is hinted at during a conversation Turing and the lone woman on his team, Joan Clarke (Keira Knightley), have with MI6 liaison Stewart Menzies (Mark Strong). For you see, in that world of secrets and subterfuge,Turing, a closeted homosexual during a time when British laws were especially draconian, surely knew how to guard confidences. Moore’s brilliant screenplay is based on Andrew Hodges book and elegantly weaves three stories — the code breaking challenge, another from Turing’s schooldays and the third that recounts his arrest on a morals charge in the early ’50s. Each of these three tales reveals a different aspect of Turing’s genius, his obsession and, ultimately, his unrelenting pain. Highly recommended.