Question 6
On the following board, we must place all the numbers, since $1$ up until $25$, following the following rules: - In each queue, the $5$ Numbers placed should form a strictly increasing sequence when read from left to right. - In each column, the $5$ Numbers placed should form a strictly increasing sequence when read from top to bottom.
The main diagonal of the board is the diagonal painted on the chart.
a) Show that after placing the numbers, the smallest number placed on the main diagonal is always greater than or equal to $5$, and the largest number placed on the main diagonal is greater than or equal to $15$.
b) Place the numbers on the board so that on the main diagonal we find the numbers $5, 9, 12, 14$ e $15$.
c) Show that it is impossible to put the numbers so that the sum on the main diagonal is less than $55$.
The main diagonal of the board is the diagonal painted on the chart.
a) Show that after placing the numbers, the smallest number placed on the main diagonal is always greater than or equal to $5$, and the largest number placed on the main diagonal is greater than or equal to $15$.
b) Place the numbers on the board so that on the main diagonal we find the numbers $5, 9, 12, 14$ e $15$.
c) Show that it is impossible to put the numbers so that the sum on the main diagonal is less than $55$.