Who designed and built the first electronic, programmable, digital computer?

The world's first programmable, electronic, digital computer was Colossus, developed by British codebreakers at the Government Code and Cypher School (Bletchley Park) in the years 1943-1945 to help solve encrypted German messages during World War II. All those in the answer options were connected with Colossus:

Max Newman led the effort to automate part of the cryptanalysis work.

Alan Turing's use of probability in cryptanalysis helped to the frame the problem that Colossus solved.

Tony Sale led a team that reconstructed a Colossus in 1994.

Tommy Flowers designed and built Colossus.

Thomas Harold Flowers (1905-1998) was an engineer with the British General Post Office (GPO). Whilst undertaking an apprenticeship in mechanical engineering he took evening classes at the University of London to earn a degree in electrical engineering. In 1926, he joined the telecommunications branch of the GPO. He studied the use of electronics for telephone exchanges and became convinced that an all-electronic system was possible.

In 1941 Alan Turing asked the GPO for help in building a decoder: Flowers was put forward. After the decoder assignment Flowers was put on a project to counter a new more sophisticated German coding system; his background in switching electronics proved crucial for the next step. Until then slow electro-mechanical systems had been used in decoding; Flowers proposed a more sophisticated electronic system using 1,800 thermionic valves. Colossus was born.