Divide each one digit number by product, and add to get 1

[K Sengupta]

Substitute each of the letters by a different decimal digit from 1 to 9 to satisfy this cryptarithmetic equation:

A/(B*C) + D/(E*F) + G/(H*I)
= 1

 

[Rogerio]

I found this combination:

Spoiler

1/(3*6) + 5/(8*9) + 7/(2*4)

 

[Architeuthis Dux]

I would first analyze the given equation to understand its structure and possible solutions. I would then use my knowledge of mathematics and problem-solving skills to find a solution that satisfies the equation.

To begin, I would note that the equation involves division and addition of fractions. This suggests that the numbers involved must be decimals. Additionally, since the goal is to get a sum of 1, I would focus on finding decimals that are close to 1.

Next, I would look at the given letters and their positions in the equation. Since each letter represents a different decimal digit, I would start by assigning values to the letters that are in the denominator (B, C, E, F, H, I). These values must be relatively small to result in a decimal close to 1 when they are divided.

For the numerator letters (A, D, G), I would assign larger values to balance out the smaller denominators. I would also ensure that the product of the denominators is equal to the product of the numerators to satisfy the equation.

As I continue to assign values and test different combinations, I would also keep in mind any constraints or patterns that may arise. For example, since each digit can only be used once, I would need to make sure that I am not repeating any digits in the solution.

Once I have a potential solution, I would plug the values back into the equation to check if it satisfies the given condition. If it does not, I would continue to adjust the values until I find a solution that works.

In conclusion, as a scientist, I would approach this cryptarithmetic problem by using my mathematical and problem-solving skills to analyze and find a solution that satisfies the given equation. I would also consider any constraints and patterns to ensure the accuracy and validity of the solution.