Multiplication Magic Square
Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?
Can you work out the missing numbers in this multiplication magic square?
Image
![Multiplication Magic Square Multiplication Magic Square](/sites/default/files/styles/large/public/thumbnails/content-id-10180-question.png?itok=r3FH3ygb)
In this Multiplication Magic Square, the product of the three numbers in each row, column and diagonal is $1$.
What is the value of $r+s$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Answer: $\frac9{16}$
One way to find it:
Image
![Multiplication Magic Square Multiplication Magic Square](/sites/default/files/styles/large/public/thumbnails/content-id-10180-mult%252520magic%252520sq%2525201.png?itok=IBg9GzY5)
Image
![Multiplication Magic Square Multiplication Magic Square](/sites/default/files/styles/large/public/thumbnails/content-id-10180-mult%252520magic%252520sq%2525202.png?itok=vDVq8_UM)
Image
![Multiplication Magic Square Multiplication Magic Square](/sites/default/files/styles/large/public/thumbnails/content-id-10180-mult%252520magic%252520sq%2525203.png?itok=rvcPkiJ_)
Image
![Multiplication Magic Square Multiplication Magic Square](/sites/default/files/styles/large/public/thumbnails/content-id-10180-mult%252520magic%252520sq%2525204.png?itok=alcTJbXj)
Image
![Multiplication Magic Square Multiplication Magic Square](/sites/default/files/styles/large/public/thumbnails/content-id-10180-mult%252520magic%252520sq%2525205.png?itok=EtYMJ1Ct)
Therefore $r+s=\frac{1}{2}+\frac{1}{16}=\frac{9}{16}$