In a magic square, the numbers in each row, the numbers in each column, and the numbers on each diagonal have the same sum. In the magic square shown, what is the value of ?
Solution
Using the second row, we see that the sum of the numbers in each row, column and diagonal must be . Since the sum of the numbers in the first column must be 9, then the bottom left number must be . Since the sum of the numbers in the top left to bottom right diagonal must be 9, then the bottom right number must be . Since the sum of the numbers in the bottom row must be 9, then and so or . We can complete the magic square as shown: \begin{tabular}{|c|c|c|} \hline 2.3 & 3.8 & 2.9 \\ \hline 3.6 & 3 & 2.4 \\ \hline 3.1 & 2.2 & 3.7 \\ \hline \end{tabular}
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.