Question 39
Place the numbers 1 through 16, without repetition, in a $4\times4$ board so that every row, column, and diagonal has the same sum, called the magic sum.
a) What is the magic sum?
b) If the sum in the squares marked $X$ below is 34, what is the sum in the squares marked $Y$?
| $Y$ | | | $Y$ |
| :--- | :--- | :--- | :--- |
| | $X$ | $X$ | |
| | $X$ | $X$ | |
| $Y$ | | | $Y$ |
c) If the board is filled with consecutive natural numbers from $k$ through $k+15$ and the magic sum is 50, find $k$.
a) What is the magic sum?
b) If the sum in the squares marked $X$ below is 34, what is the sum in the squares marked $Y$?
| $Y$ | | | $Y$ |
| :--- | :--- | :--- | :--- |
| | $X$ | $X$ | |
| | $X$ | $X$ | |
| $Y$ | | | $Y$ |
c) If the board is filled with consecutive natural numbers from $k$ through $k+15$ and the magic sum is 50, find $k$.