Please help me. Insert 9 different digits 1, 2, 3, ..., 9 into 9 empty cells so that the 3 equalities across and the 3 vertical equalities are satisfied. Note that the operations in each equality are always performed from left to right (or from top to bottom), but not in accordance with the usual order of operations. For example, 2+4×5=(2+4)×5=6×5=30, but not 2+4×5=2+(4×5)=2+20=22.

      C1        C2        C3

R1    6          2           5

R2    8          1           9

R3    3          4          7

Step-by-step explanation:

It is given that we have to insert 9 different digits 1, 2, 3, ..., 9 into 9 empty cells so that the 3 equalities across and the 3 vertical equalities are satisfied.

Note : The operations in each equality are always performed from left to right (or from top to bottom), but not in accordance with the usual order of operations.

Factors of 49 = 7 × 7, so element of R3 and C3 must bw 7.

Now,

Sum of remaining elements of R3 = 7 = 3 + 4

Sum of remaining elements of C3 = 14 = 5 + 9

Let R1C3 = 5, R2C3 = 9, R3C1 = 3, R3C2 = 4.

Therefore, the required elements are:

      C1        C2        C3

R1    6          2           5

R2    8          1           9

R3    3          4          7

associative property of multiplication