Math Problem Statement

Which of the options below follows next in the sequence shown?

Solution

The sequence in this question shows dots moving systematically on a square grid. Let's analyze the pattern:

  1. The first box has a dot in the top-left corner.
  2. The second box has a dot in the bottom-left corner.
  3. The third box has two dots: one in the bottom-left corner (same position as the previous step) and the second one in the top-right corner.
  4. The fourth box has two dots: one in the bottom-right corner and the second one in the top-right corner.

Pattern Explanation:

  • The first dot starts in the top-left corner and moves clockwise around the perimeter of the square, going from the top-left to bottom-left to bottom-right, etc.
  • In each frame, either one or two dots appear, and the next dot appears after a clockwise shift.
  • By the third frame, a second dot is introduced in the top-right corner. Both dots move similarly clockwise.

Given this reasoning, the next step should feature two dots, one in the bottom-right corner (continuing its clockwise movement) and another in the bottom-left.

The correct answer is the top-right option in the grid of choices, which has dots in the top-left and bottom-left corners.

Would you like more details, or have any other questions?

Here are some related questions to extend your thinking:

  1. How would you generalize the movement of dots for larger grids?
  2. Can you find other sequences that alternate between single and double dots?
  3. What patterns would emerge if the dots moved in a counter-clockwise direction?
  4. How would you identify a repeating cycle within this sequence?
  5. What role does symmetry play in these types of visual puzzles?

Tip: When analyzing sequences like these, look for directional movement and how the number of elements (dots) changes between steps.

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Math Problem Analysis

Mathematical Concepts

Pattern Recognition
Geometric Transformations

Formulas

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Theorems

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Suitable Grade Level

Grades 5-7