NOTE: In the addition rule for number base, the digits which makes up a base can not be equal to or greater than the base. Also, if the digit is equal to or greater than the base, we are to divide the digit by the base and right down the remainder, while the quotient (result of the division) is carried to the next addition.

The addition of 5, 4 and 5 is 14. The result of the addition, as seen in the question, is 0. What number will divide 14 to give us a remainder 0? Since one of the digits in the addition is 6, it means that the base can not be 6 or any other number less than 6. So we try dividing the 14 by 7. Diving 14 by 7, gives 2 with 0 as remainder. The remainder 0 was written and the 2 carried over to the next addition.

Next, addition of 6, 2 and 2 gives 10. Adding the 2 carried over from the addition of 5,4 and 5, we get 12. Try dividing the 12 by 7 which we used before. The result of the division is 1 remainder 5. The remainder 5 was written while the answer which is 1, is carried over to the next addition.

Since we used 7 to divide for the digits added earlier, we still try it for the last addition to ascertain if it will give the 0 as indicated in the question.

Addition of 4 and 2 is 6. Adding the 1 carried over from the previous addition, we get 7. Dividing the 7 by 7, we get 1 remainder 0. Usually, the remainder is written while the result is carried over. We write the remainder and carry over the 1. Since there is no other addition to be carried out, the 1 is dropped after 0.

The explanation above shows that the base in which the addition was done is base 7.