3/19/2025Did You Find Out? Get the Answer to the Riddle of PA E-News Issue No. 1, September 2025

What numbers are we looking for?

We are looking for two-digit natural numbers that are equal to the product of their first digit increased by 1 and their second digit increased by 2. These numbers must not start with 0. Can you find out which numbers these are?

Solution

A two-digit number consists of the two digits A and B and its value is 10A + B. For the numbers we are looking for, this should be equal to the product of A + 1 and B + 2. This means that 10A + B = (A + 1)(B + 2). This can be rearranged to A(8 - B) = 2. Now the following applies: the left-hand side of the equation is only 2 if one of the two factors is 1 and the other factor is 2. Consequently, either A = 1 and B = 6 or A = 2 and B = 7. The numbers we are looking for here are therefore 16 and 27.