|Spoiler Inside: Solution to Puzzle||SelectShow>|
Name each of the statements with the initial of the stater and the number of his statement. Tom’s first statement is T1, etc.
Assume that Tom is the truthteller. This is contradicted by T2.
Assume that Dick is the truthteller. By this, T1 is false. By D2, H1 is false. T2 and H2 are of opposite truth values, and it turns out not to matter which is which. By this, Harry is the murderer.
Assume that Harry is the truthteller. By H2, Tom is the liar. Dick is the alternator. By H1, D2 must be false, so D1 is true. This leaves Tom as the murderer.
So Dick did not do it, but we can not determine any further.