To solve the 4x4 magic square puzzle where each row, column, and diagonal sums to 34, the arrangement of the numbers from 1 to 16 can be organized as follows:

16  2  3  13
5  11  10  8
9  7  6  12
4  14  15  1

Verification:

• Rows:

  • Row 1: $16 + 2 + 3 + 13 = 34$
  • Row 2: $5 + 11 + 10 + 8 = 34$
  • Row 3: $9 + 7 + 6 + 12 = 34$
  • Row 4: $4 + 14 + 15 + 1 = 34$

• Columns:

  • Column 1: $16 + 5 + 9 + 4 = 34$
  • Column 2: $2 + 11 + 7 + 14 = 34$
  • Column 3: $3 + 10 + 6 + 15 = 34$
  • Column 4: $13 + 8 + 12 + 1 = 34$

• Diagonals:

  • Diagonal 1: $16 + 11 + 6 + 1 = 34$
  • Diagonal 2: $13 + 10 + 7 + 4 = 34$

This arrangement successfully meets the requirement of the puzzle.

Would you like any further details or explanations about magic squares? Here are some questions you might consider:

1. What are the properties of a magic square?
2. How can you generate a magic square of different sizes?
3. What strategies can be used to solve similar logic puzzles?
4. Are there other methods to arrange numbers in a grid to meet certain conditions?
5. What is the history of magic squares in mathematics?

Tip: To create a magic square of odd order, consider using the Siamese method, where you place numbers starting from the middle of the top row and move diagonally.