24 Game

Four Chips to Twenty-Four

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The statement here is our own: the same inputs, outputs and technique.

A tabletop puzzle deals four numbered chips, given in cards, each showing a digit from 1 to 9.

The aim is to write an arithmetic line worth exactly 24 under these rules:

Each chip's number is used once and once only. The chips may be taken in any order.
The four numbers are joined by three operators, each chosen freely from +, -, * and /, and brackets may be placed however you like.
Division is ordinary division, not whole-number division, so a partial value such as one third is perfectly legal as long as the line finishes at 24. Dividing by zero is not allowed, and a zero can turn up as a partial value, for instance from a chip subtracted from an equal chip.
No two chips may be written side by side to make a two-digit number, and no number may be given a leading minus sign of its own.

All arithmetic is exact, and the line has to come to 24 exactly rather than close to it. Return true when such a line exists and false otherwise.

Examples

Example 1

The line 5 * (5 - 1 / 5) is worth 24, since 1 / 5 is one fifth, 5 minus one fifth is four and four fifths, and five times that is 24.

Example 2

Every line that can be written from four ones is worth at most 4, so 24 is out of reach.

Example 3

The line 1 * 2 * 3 * 4 is worth 24.

The editor starts with this. It matches the parent problem's shape, so a solution that works here works on a standard judge unchanged.

Python

def judge_point24(cards: list[int]) -> bool:

Java

public boolean judgePoint24(int[] cards)