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Seven different single-digit numbers are written in the circles of the diagram shown with one number in each circle. The product of the three numbers in each of the three lines of three numbers is the same. Which number is written in the circle containing the question mark?​

User Royland
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Answer:

Without an image or a more detailed description of the diagram, it's difficult to provide an exact answer to this problem. However, we can use some logical reasoning to try to solve it.

Let's assume that the three lines of three numbers are arranged in a Tic-Tac-Toe grid, like this:

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A B C

D E F

G H I

We know that the product of the three numbers in each line is the same. Let's call this product "P". Then we can write:

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A * B * C = P

D * E * F = P

G * H * I = P

If we divide the second equation by the first equation, we get:

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(D * E * F) / (A * B * C) = 1

Since all the numbers are single-digit, this means that either D or F is equal to A, B, C, or 1. If D or F is equal to 1, then E is also equal to 1, which means that the entire middle row is filled with 1s, and that cannot be the case since all the numbers are different.

Therefore, we can assume that either D or F is equal to one of the numbers in the top row. Without further information, we cannot determine which one it is, but we know that the product of the numbers in the bottom row must be divisible by the product of the numbers in the top row. This means that the number in the circle containing the question mark must be a factor of this product, and it must be different from all the other numbers in the diagram.

Again, without more information, we cannot determine the exact number in the circle containing the question mark, but this logic should help narrow down the possibilities.

Explanation:

User SantiG
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