Question

A number has two digits. If these two digits are multiplied, their product is equal to half the original number.
What was the original number?

Answer 1

Answer:

To solve this problem we must realize a system to represent our problem, we have:    
                           
                                                   ab = 2 · a · b

We decompose the number ab, we have:      
       
             (10 · a) + b = 2 · a · b       
               10 · a = 2 · a · b - b

 We take common factor b, we have:          
        
               10 · a = b · (2a-1)

 Decompose the number 10:  
               
                5 · 2 · a = b · (2a-1)

We perform coefficient equalization between 5 and 2a-1 because this equality is met, the two will always be odd:

                                                          5 = 2a-1
                                                            a = 3

Then b = 6

The number is 36, the multiplication of your digits is 18 and this is your half.