Anti Magic Square

Question

Are the two examples of $4\times 4$ anti-magic squares currently on Wikipedia actually anti-magic squares under the definition given there?

The examples are:

$$\left[ \begin {array}{cccc} 2&15&5&13\\16&3&7&12\\ 9&8&14&1\\ 6&4&11&10 \end {array} \right]$$

and $$\left[ \begin {array}{cccc} 1&13&3&12\\15&9&4&10\\ 7&2&16&8\\ 14&6&11&5 \end {array} \right]$$

Answer 1

For example, for the first one: $$\left[ \begin {array}{cccc} 2&15&5&13\\16&3&7&12\\ 9&8&14&1\\ 6&4&11&10 \end {array} \right] $$

The entries are the integers $1$ to $16$.

The rows sum to 35, 38, 32, 31 respectively, the columns to 33, 30, 37, 36, and the diagonals to 29, 34. These are the 10 consecutive integers 29 to 38.

So yes, it satisfies the definition.

Answer 2

I wrote a program to evaluate the sums, and got, for the first example:

29 Left/right diagonal
30 col 2
31 row 4
32 row 3
33 col 1
34 Right/left diagonal
35 row 1
36 col 4
37 col 3
38 row 2

For the second example:

29 row 1
30 col 2
31 Left/right diagonal
32 Right/left diagonal
33 row 3
34 col 3
35 col 4
36 row 4
37 col 1
38 row 2

So it looks fine.