How many US supreme court justices are needed to decide to take a case as a function of the number of total justices, and how was that decided?

Question

In CNN's February 10, 2024 Why the Supreme Court may not hear Trump’s immunity appeal, senior legal analyst and former federal prossecutor Ellie Honig says

...but (this is) really important for people to keep in mind; of course you need five of nine justices to win a supreme court case, but you only need four to take the case.

Question: How many US supreme court justices are needed to decide to take a case as a function of the number of total justices, and how was that decided?

• Is it always four, or is it defined as the majority number minus one, or something else? (The number of justices on the supreme court is not necessarily fixed at nine).
• Is the number (or method to calculated it) needed to take the case specified in the US constitution? Was there debate on that number? How was it arrived upon?

What might not have been anticipated is the size of the workload of the Supreme Court and how it has expanded over the centuries, and the number required to accept might be thought of as a "throttle" on that.

Answer 1

The "rule of four" is a customary internal practice adopted by the Court on its own volition.

The rule of four is not required by the US Constitution, any law, or even the Court's own published rules. Rather, it is a custom that has been observed since the Court was given discretion on hearing appeals

The justices have never said how they set the threshold or whether it is based on a function that depends on the size the court. But as far as we can tell as outside observers, the threshold is not lower when the court has a membership of eight, or when justices recuse themselves from a certiorari decision.