Question 1

We need to follow the given rules to select numbers. Then we will multiply all the selected numbers.

Step 1 — Understanding the Game Rules

Let us understand how to play this game. First, we circle any number in the grid. Then, we strike out its row and its column. Next, we circle any unstruck number. We repeat striking out its row and column. We continue until all numbers are struck out. Finally, we multiply all the circled numbers.

Step 2 — Following the Example Rounds

The example shows us how to play. In Round 1, the number -6 is circled. Its row (Row 1) and column (Column 4) are struck out. In Round 2, the number 14 is circled. Its row (Row 2) and column (Column 2) are struck out. In Round 3, the number 20 is circled. Its row (Row 4) and column (Column 1) are struck out. In Round 4, the number 18 is circled. Its row (Row 3) and column (Column 3) are struck out. Now, all numbers are struck out.

Step 3 — Listing the Circled Numbers

From the example, we can see the circled numbers. The first circled number is -6. The second circled number is 14. The third circled number is 20. The fourth circled number is 18. These are the numbers we need to multiply.

Step 4 — Multiplying the Circled Numbers

We will multiply the four circled numbers. The numbers are -6, 14, 20, and 18. Let us multiply them step by step.

First, multiply -6 by 14. $(-6) \times 14$ $= -(6 \times 14)$ $= -84$

Next, multiply -84 by 20. $(-84) \times 20$ $= -(84 \times 20)$ $= -(84 \times 2 \times 10)$ $= -(168 \times 10)$ $= -1680$

Finally, multiply -1680 by 18. $(-1680) \times 18$ $= -(1680 \times 18)$ $= -(1680 \times (10 + 8))$ $= -(1680 \times 10 + 1680 \times 8)$ $= -(16800 + 13440)$ $= -(30240)$

$\boxed{\mathbf{-30240}}$

Answer

(i) The final product of the circled numbers is -30240.