Suppose you’re given a matrix with 5 columns and 3 rows. The challenge is to fill it with integers from 0 to 9 such that every row adds up to 20, and every column adds up to 10. Take a moment to try this puzzle.
I claim that it is impossible to solve this puzzle. Let’s check the math to understand why.
Observe that each row adds up to 20. this implies the sum of all numbers in the matrix is 20 times 3, which equals 60.
Also, each column adds up to 10. With 5 columns, that gives us 10 times 5 = 50 as the sum of all numbers.
And this is the issue. The sum of all numbers in a matrix can not have two different values. Hence, this puzzle is impossible to solve.
This puzzle serves as a reminder for coding enthusiasts who tend to rely on computation over mathematics. No matter how simple or complex a problem looks, it’s always worth stepping back and analyzing the structure for useful insights. Without analysis, we risk wasting both time and computational resources.
Music by Sergio Prosvirini from Pixabay