Can You Solve This Math Puzzle? Test Your Skills Like a Pro 2026

Can you solve this math puzzle that stumps most adults? A 3x3 grid filled with positive whole numbers, where each row and column multiplies to 30. It's a challenge from the world's smartest teen, and the answer is more than 200 ways. In this article, we'll break down the puzzle, explore the logic, and provide a step-by-step solution.

Understanding the 3x3 Grid Puzzle

The puzzle asks: How many ways can you fill a 3×3 grid with positive whole numbers such that the product of the numbers in each row and each column is 30? Each cell must contain a positive integer, and the three numbers in each row or column do not need to be distinct.

This problem comes from Alex Chui, a British student who recently became the most successful contestant in the history of the International Mathematical Olympiad (IMO). He scored a perfect 42/42 at this year's event in Shanghai, earning his seventh consecutive medal.

Why This Puzzle Is So Elegant

At first glance, you might think to brute-force count every grid. But that's impractical—there are over 200 solutions. The beauty lies in the underlying number theory and combinatorics. You need to factor 30 into its prime components: 2 × 3 × 5. Every number in the grid must be a divisor of 30, because if any cell had a factor outside {1,2,3,5,6,10,15,30}, the row product would exceed 30.

So each cell is one of these eight possible values. The challenge is to arrange them so that each row and column product equals 30. This is a classic example of a multiplicative magic square variant.

Step-by-Step Approach to Solve

To solve systematically, consider the prime factorization. Each row and column must contain exactly one factor of 2, one factor of 3, and one factor of 5. That means each row and column must have a number divisible by 2, a number divisible by 3, and a number divisible by 5—but they can be combined in the same cell (like 6, 10, 15, or 30).

One effective method is to first place the number 30 in a cell, which automatically satisfies that row and column. Then fill the remaining cells with combinations of 1,2,3,5,6,10,15. But you must ensure that each row and column still has the right prime factors.

Using a Table to Visualize Possibilities

Here's a comparison of possible cell values and their prime factor contributions:

Using this table, you can systematically assign numbers to cells. The total number of valid grids is 216, as confirmed by combinatorial enumeration. The puzzle is a great exercise in logical deduction and systematic counting.

Key Takeaways for Puzzle Solvers

• Prime factorization is the key to solving multiplicative grid puzzles.
• Always consider that numbers can be combined (like 6, 10, 15) to satisfy multiple prime requirements.
• Start with the most restrictive cell (like 30) to reduce possibilities.
• Use a table to track prime factors across rows and columns.
• Practice with smaller grids (2x2) to build intuition before tackling 3x3.

Why This Puzzle Matters for Cognitive Skills

Solving such puzzles improves your mathematical reasoning, pattern recognition, and patience. It's the same kind of thinking that Olympiad champions like Alex Chui use to solve complex problems under time pressure. Even if you don't get all 216 solutions, attempting the puzzle strengthens your brain. The background to this story is set out in Reading for Pleasure Boosts Memory, Math Skills and Mental Health.

FAQ: Common Questions About the 3x3 Grid Puzzle

Now that you know the solution, try to create your own variations. Change the product to 60 or 90 and see how the number of solutions changes. The world of mathematical puzzles is vast, and this one is a gem from a true prodigy.

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