1. My age is a two-digit number that is a power of 5 . My cousin's age is a two-digit number that is a power of 2 . The sum of the digits of our ages is an odd number.
What is the product of the digits of our ages?
Solution
240

My age must be 25 . My cousin's age is a two-digit power of two, so is 16,32 or 64 . The sums of the digits of our ages would then be 14,12 and 17 respectively. Since this sum must be odd my cousin's age must be 64 . Therefore the product of the digits of our ages is $2 \times 5 \times 6 \times 4=240$.