MathDB
Multiplication magic square

Source: 2021 Nigerian MO Round 3/P4

December 19, 2022
multiplicationcombinatorics

Problem Statement

In the multiplication magic square below, l,m,n,p,q,r,s,t,ul, m, n, p, q, r, s, t, u are positive integers. The product of any three numbers in any row, column or diagonal is equal to a constant kk, where kk is a number between 11,00011, 000 and 12,50012, 500. Find the value of kk. \begin{tabular}{|l|l|l|} \hline ll & mm & nn \\ \hline pp & qq & rr \\ \hline ss & tt & uu \\ \hline \end{tabular}