In a magic square, the sum of the numbers in each row, column, and diagonal is the same. This number is called the magic sum. In the following magic square, \(A\), \(B\), \(C\), \(D\), \(E\), \(F\), \(G\), \(H\), and \(J\) represent numbers, and clues are given to determine some of these numbers.
| \(A\) | \(B\) | \(C\) |
| \(D\) | \(E\) | \(F\) |
| \(G\) | \(H\) | \(J\) |
The value of \(A\) is one more than the product of \(3\) and \(4.\)
The value of \(B\) is the sum of \(1\), \(2\), and \(3.\)
The value of \(C\) is the smallest odd number greater than \(10.\)
The value of \(F\) is also known as a dozen.
The value of \(G\) is equal to the total number of sides in three triangles.
Use the given clues to determine the values for \(A\), \(B\), \(C\), \(F\), and \(G\).
Determine the magic sum for this magic square, then use this to complete the magic square.
Would you have been able to complete this magic square if only four clues were given, instead of five? If so, which clue(s) do you not need?
Theme: Number Sense