Question 153
Suppose that we fill a $3 \times 3$ table with natural numbers from $1$ to $9$ using each of them precisely once. After that, we write down the sums in each of the four $2 \times 2$ squares in the ascending order. Determine whether it is possible to obtain the following quadruples of natural numbers:
a) $24$, $24$, $25$, $25$,
b) $20$, $23$, $26$, $29$.
a) $24$, $24$, $25$, $25$,
b) $20$, $23$, $26$, $29$.