Magic square logic puzzle

Make a \(5 \times 5\) magic square using the following clues:

• Perfect squares are in b5, d3, b1, and c1.
• Prime numbers are in a5, c5, e5, c4, a3, c3, e3, e2, and a1.
• Triangular numbers are in d5, e4, d3, a1, e1, and c2.
• Perfect cubes are in d3 and b2.
• Powers of 2 are in b5, b2, e2, and b1.
• Two-digit palindromic numbers are in a5 and d1.
• Factors of 100 are in b5, d5, c4, b3, d3, a2, and e2.
• The median of all the numbers is in c3.
• Row 3 and column c are all odd.
• Numbers that are the same upside-down are in a5, d3, and b2.

Print out a few of these so you don't have to redraw the grid for each attempt. Contact me if you need the TikZ code for that PDF.