10. The smallest four two-digit primes are written in different squares of a $2 \times 2$ table. The sums of the numbers in each row and column are calculated.
Two of these sums are 24 and 28 .
The other two sums are $c$ and $d$, where $c<d$.
What is the value of $5 c+7 d$ ?
Solution
412

The only way of obtaining sums of 24 and 28 are using $11+13=24$ and $11+17=28$. One possible configuration is shown in the diagram, with other two sums $c=13+19=32$ and $d=17+19=36$. The value of $5 c+7 d$ is $5 \times 32+7 \times 36=412$.