# The Paradox Engine

Five engineers — Ada, Babbage, Church, Dijkstra, and Euler — built a machine with five components: the Clock, the Memory, the Gate, the Register, and the Bus.

## The Setup

1. Each engineer built exactly one component (a bijection).
2. Each component has a state: **stable** or **unstable**.
3. Each engineer's truthfulness depends on the stability of the component they built:
   - If their component is stable, they tell the truth.
   - If their component is unstable, they lie.
4. The machine functions if and only if an **odd** number of components are stable.

## The Dependency Graph

The components' stabilities are interdependent:

- **Clock** is stable iff Memory is unstable
- **Memory** is stable iff exactly one of {Gate, Register} is stable
- **Gate** is stable iff Register is stable or Bus is stable (or both)
- **Register** is stable iff it is NOT the case that both Bus and Clock are stable
- **Bus** is stable iff Gate is unstable

## The Statements

**Ada:** "I built the Clock."

**Babbage:** "Ada built a stable component."

**Church:** "Dijkstra built the Memory."

**Dijkstra:** "Euler built the Register."

**Euler:** "Babbage built the Gate."

## The Question

Determine:
1. Which engineer built which component
2. The stability of each component
3. Whether the machine functions

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*This puzzle has exactly one solution.*