Question 11
Emerald writes the integers from $1$ to $9$ in a $3 \times 3$ table, one number in each cell, each number appearing exactly once. Then she computes eight sums: the sums of three numbers on each row, the sums of the three numbers on each column and the sums of the three numbers on both diagonals.
a. Show a table such that exactly three of the eight sums are multiples of $3$.
b. Is it possible that none of the eight sums is a multiple of $3$?
a. Show a table such that exactly three of the eight sums are multiples of $3$.
b. Is it possible that none of the eight sums is a multiple of $3$?