There are a number of dice, and the input array contains the number on the dice's face up. Dice is 6 faced. Calculate the total number of minimum rotations of dice, to make all faces the same. 1 will require only one rotation to have 2, 3, 4 and 5 face up, but would require minimum two rotations to make it the face 6, as 6 is the opposite side of 1. The opposite side of 2 is 5 and 3 is 4.
I have come up with a solution, but I believe there should be a better solution.
For example:
A = {1,1,6}, Answer = 2. Rotate 6 two times to get 1.A = {1,2,3}, Answer = 2. Rotate 1 and 2 and make them 3.A = {1,6,2,3}, Answer = 3. Rotate 1, 6 and 3 to make them all 2.
import java.util.*;
public class DiceProblem {
    public static void main(String args[]){
    int[] A = {3,4,1,2,4,2,3,5,1,2,3,4,6,2,4,1,5,2};
    Map<Integer, Integer> countMap = new HashMap<>();
    int rotation = 0;
    int diceCount;
    int maxDiceNumber = A[0];
    int OppositeOfMaxDiceNumber;
    int max = 1;
    for(int i = 1; i <= 6 ; i++){
        diceCount = 0;
        for (int value : A) {
            if(i == value){
                diceCount++;
            }
        }
        countMap.put(i, diceCount);
        if(diceCount > max){
            max = diceCount;
            maxDiceNumber = i;
        }
    }
    if(max == 1){
        if(countMap.get(1).equals(countMap.get(6)) && countMap.get(1) != 0 && countMap.get(2) != 0){
            maxDiceNumber = 2;
        }else if(countMap.get(2).equals(countMap.get(5))  && countMap.get(2) != 0 && countMap.get(3) != 0){
            maxDiceNumber = 3;
        }else if(countMap.get(3).equals(countMap.get(4)) && countMap.get(1) != 0){
            maxDiceNumber = 1;
        }else if(countMap.get(2) != 0){
            maxDiceNumber = 2;
        }else if(countMap.get(5) != 0){
            maxDiceNumber = 5;
        }else if(countMap.get(6) != 0){
            maxDiceNumber = 6;
        }
    }
    System.out.println("Max Dice Number: "+ maxDiceNumber);
    OppositeOfMaxDiceNumber = createOpposite(maxDiceNumber);
    System.out.println("Opposite Dice Number: "+ OppositeOfMaxDiceNumber);
    Iterator it2 = countMap.entrySet().iterator();
    while (it2.hasNext()) {
        Map.Entry pair = (Map.Entry)it2.next();
        System.out.println(pair.getKey() + " = " + pair.getValue());
        if((int)(pair.getValue()) > 0 && (int)(pair.getKey()) != maxDiceNumber){
            if((int)(pair.getKey()) == OppositeOfMaxDiceNumber){
                rotation = rotation + (2  * (int)(pair.getValue()));
            }else {
                rotation = rotation + ((int)(pair.getValue()));
            }
        }
        it2.remove(); // avoids a ConcurrentModificationException
    }
    System.out.println("Number of Minimum Rotations: "+ rotation);
}
private static int createOpposite(int key){
    switch (key) {
        case 1:
            return 6;
        case 2:
            return 5;
        case 3:
            return 4;
        case 4:
            return 3;
        case 5:
            return 2;
        case 6:
            return 1;
    }
    return 0;
}}
public class DiceProblem {
    public static void main(String args[]){
        int[] A = {3,4,1,2,4,2,3,5,1,2,3,4,6,2,4,1,5,2};
        int flip_count;
        int min_flip_count = 9999999;
        for (int value : A) {
            flip_count = 0;
            for (int i : A) {
                if (value == i) {
                    flip_count += 0;
                } else if (value + i == 7) {
                    flip_count += 2;
                } else {
                    flip_count += 1;
                }
            }
            if (flip_count < min_flip_count) {
                min_flip_count = flip_count;
            }
        }
        System.out.println("Minimum Flip Count:" + min_flip_count);
    }
}
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