When I was a boy, my grandfather used to give me puzzles for me to solve. The following puzzle is one of them.
A magic square is an arrangement of numbers from 1 to n² in an n² matrix in which each number should only occur once. Every row, column, and diagonal of a magic square have the same sum called the magic sum. The most popular magic square is the 3 × 3 magic square, also known as the Lo Shu Square:
It contains the numbers 1 to 9 and each row, column and diagonal of this magic square has a magic sum of 15.
While there are systematic methods for solving magic squares, you don’t need to know anything about them to solve this particular magic square as it can be solved by trial and error.
Now, here’s the puzzle my grandfather challenged me to solve:
When solving a regular 3 × 3 magic square, you would find that the number 8 must be in one of the corners of the magic square. The challenge is this: Can you create a magic square wherein the number 8 is on the top center (same confitions for constructing a 3 × 3 magic square apply) as shown:
Before you tell me that this is not an acceptable solution, remember that this solution has met all the conditions of the puzzle. Even if there are fractions, it still complied with the conditions that only numbers from 1 through 9 should be used and each number should only be used once. If I said that fractions are not allowed, then this puzzle would most likely be unsolvable. The solution is not obvious to most people which made this puzzle difficult.
When my grandfather showed this puzzle to me, I immediately said that it’s impossible to solve it. I know how to construct magic squares so I was sure that his puzzle has no valid solution. He just laughed and encouraged me to try harder.
Days, then weeks had gone by and I got nowhere in answering it. Then I began to pester him to tell me the answer. However, my grandfather would never spoil his puzzles so he just ignored my requests.
But as weeks became months, I set aside the puzzle at some point and ceased to think about it as I was distracted by more puzzles from my grandfather, books, several hobbies, and other diversions. A few more months later, my grandfather passed away.
I felt so dismal about it since we were very close and it was the first time I experienced how it felt to lose a loved one. During that time, I suddenly remembered this particular unsolved puzzle and tried again. It took me more than a week to solve it. I’m not sure if this is the solution my grandfather wanted, but I believe that this is it.
Solving puzzles for my grandfather was one of my most cherished childhood memories. Seeing his joyful smile every time I solved a puzzle was enough to make me happy. No matter where he is now, I hope that he would somehow know that I finally solved this puzzle.