Issue with Separating Combinations into Vectors in C+

I have a vector of 16 pairs of symbols and colors, where there are 4 different colors and 4 different symbols. I need to separate these combinations into 4 different vectors, with the following conditions:

A symbol cannot have the same color as another symbol in the same vector. A color cannot have the same symbol as another color in the same vector. A combination of symbol and color can only be used once in the 4 vectors. I have tried implementing the separation logic in C++, but I'm encountering an issue where sometimes, some combinations are not being assigned to any vector, even though it should be possible to assign them.

I have already tried shuffling the combinations randomly using random_shuffle and have checked the logic for validity. However, the problem still persists, and I'm unable to identify the cause.

Could someone please help me identify the issue and provide a solution to ensure that all combinations are assigned to the vectors while satisfying the given conditions? I appreciate any guidance or suggestions. Thank you!

#include <iostream>
#include <vector>
#include <algorithm>
#include <cstdlib>
#include <ctime>

using namespace std;

vector<char> symbols = {'&', '#', '%', '$'};
vector<char> colors = {'R', 'G', 'B', 'Y'};
vector<pair<char, char>> combinations;

void separateVectors() {
    // Shuffle the combinations randomly
    srand(time(0));
    random_shuffle(combinations.begin(), combinations.end());

    vector<vector<pair<char, char>>> vectors(4); // Store the four separate vectors

    for (const auto& combination : combinations) {
        bool assigned = false; // Flag to indicate if the combination has been assigned

        // Iterate over the vectors to find a suitable one for the current combination
        for (int i = 0; i < 4; i++) {
            bool valid = true;

            // Check if the symbol or color already exists in the current vector
            for (const auto& pair : vectors[i]) {
                if (pair.first == combination.first || pair.second == combination.second) {
                    valid = false;
                    break;
                }
            }

            // If the combination satisfies the conditions, add it to the current vector and update the flag
            if (valid) {
                vectors[i].push_back(combination);
                assigned = true;
                break;
            }
        }

        // If the combination couldn't be assigned to any vector, print a warning
        if (!assigned) {
            cout << "Warning: Combination (" << combination.first << ", " << combination.second << ") couldn't be assigned." << endl;
        }
    }

    // Print the four separate vectors
    for (int i = 0; i < 4; i++) {
        cout << "Vector " << i << endl;
        for (const auto& pair : vectors[i]) {
            cout << "Symbol: " << pair.first << " Color: " << pair.second << endl;
        }
        cout << endl;
    }
}

int main() {
    // Generate all possible combinations
    for (const auto& symbol : symbols) {
        for (const auto& color : colors) {
            combinations.push_back(make_pair(symbol, color));
        }
    }

    separateVectors();

    return 0;
}

Expected Output: The expected output should be four separate vectors, each containing four combinations of symbol and color, satisfying the given conditions. Example:

Vector 0
Symbol: # Color: Y
Symbol: $ Color: R
Symbol: & Color: B
Symbol: % Color: G

Vector 1
Symbol: # Color: R
Symbol: & Color: Y
Symbol: % Color: B
Symbol: $ Color: G

Vector 2
Symbol: # Color: G
Symbol: % Color: Y
Symbol: & Color: R
Symbol: $ Color: B

Vector 3
Symbol: & Color: G
Symbol: # Color: B
Symbol: $ Color: Y
Symbol: % Color: R

Current Output: The current output is not assigning some combinations to any vector, even though it should be possible to assign them. Example:

Warning: Combination ($, Y) couldn't be assigned.
Warning: Combination (&, B) couldn't be assigned.
Vector 0
Symbol: # Color: G
Symbol: $ Color: B
Symbol: % Color: R
Symbol: & Color: Y

Vector 1
Symbol: # Color: B
Symbol: & Color: G
Symbol: % Color: Y
Symbol: $ Color: R

Vector 2
Symbol: % Color: G
Symbol: & Color: R
Symbol: # Color: Y

Vector 3
Symbol: % Color: B
Symbol: $ Color: G
Symbol: # Color: R

Additional Notes:

I have verified the logic for checking validity and assigning combinations to vectors, but the issue still persists. The issue only occurs like 50% of the time, most of the time, the combinations are missing from the vector 2 and 3, rarely from 0 and 1. Sometimes there are up to 5 combinations not assigning but most of the time it's only one or two.

I would greatly appreciate any insights, suggestions, or solutions to resolve this problem. Thank you in advance for your help!