## Numerical Puzzle

The five-square numerical puzzle below requires the vertical column to be filled with the digits from a three-digit integral power of $5$ and the horizontal row to be filled with the digits from a three-digit integral power of $2$. What digit will be in the shaded square?

Source: NCTM Mathematics Teacher, February 2008

Solution
$5^2=25\quad 5^3=125\quad 5^4=625\quad 5^5=3125$
$2^6=64\quad 2^7=128\quad 2^8=256\quad 2^9=512\quad 2^{10}=1024$

Answer: $6$