How to guarantee the problem is valid?

"""
Preprocess dataset for countdown task - given a target number and N numbers, generate equations to reach target
"""

import re
import os
from datasets import Dataset, load_dataset
from random import randint, seed, choice
from typing import List, Tuple
from tqdm import tqdm
from verl.utils.hdfs_io import copy, makedirs
import argparse


def gen_dataset(
    num_samples: int,
    num_operands: int = 6,
    max_target: int = 1000,
    min_number: int = 1,
    max_number: int = 100,
    operations: List[str] = ['+', '-', '*', '/'],
    seed_value: int = 42,
) -> List[Tuple]:
    """Generate dataset for countdown task.
    
    Args:
        num_samples: Number of samples to generate
        num_operands: Number of numbers provided in each sample
        max_target: Maximum value for target number
        min_number: Minimum value for provided numbers
        max_number: Maximum value for provided numbers
        operations: List of allowed operations
        seed_value: Random seed for reproducibility
        
    Returns:
        List of tuples containing (target, numbers, solution)
    """
    seed(seed_value)
    samples = []
    
    for _ in tqdm(range(num_samples)):
        # Generate random target
        target = randint(1, max_target)
        
        # Generate random numbers
        numbers = [randint(min_number, max_number) for _ in range(num_operands)]
        
        
        samples.append((target, numbers))
    
    return samples