1. **State the problem:** We want to find the number of squares in the 35th layer of a tiling pattern where the first layer has 1 square, the second has 5 squares, the third has 13 squares, and the fourth has 25 squares. 2. **Identify the pattern:** The number of squares in each layer forms a sequence: 1, 5, 13, 25, ... 3. **Analyze the pattern:** Notice the pattern corresponds to the squares forming a diamond shape with side length $2n-1$ for layer $n$. 4. **Formula:** The total number of squares in layer $n$ is given by the square of the side length: $$\text{Squares in layer } n = (2n - 1)^2$$ 5. **Apply the formula for $n=35$:** $$ (2 \times 35 - 1)^2 = (70 - 1)^2 = 69^2 $$ 6. **Calculate $69^2$:** $$ 69^2 = 69 \times 69 = 4761 $$ 7. **Conclusion:** The 35th layer contains 4761 squares. **Note:** The options 1649 and 1823 do not match the pattern or formula derived, so the correct answer is 4761 squares, which is not listed among the options.