Short Answer 
The painting pattern consists of a sequence of 1 blue square, 2 red squares, and 3 green squares, repeating every 6 squares. Within 100 squares, there are 16 complete cycles, and the highest numbered square painted blue is square 97.
Understand the Painting Sequence
The painting pattern follows a specific order that includes three different colors applied in a fixed sequence. The order is:
- 1 blue square
- 2 red squares
- 3 green squares
This cycle repeats every 6 squares. Therefore, it is crucial to recognize that the formation continues indefinitely across the board, which consists of 100 squares.
Calculate Complete Repetitions
To determine how many complete cycles fit within the 100 squares, you need to divide the total number of squares by the length of the sequence. The calculation is:
- Total squares: 100
- Length of one sequence: 6
- Maximum complete repetitions: 100 / 6 = 16 remainder 4
This means that the painting sequence completes 16 complete cycles, filling the first 96 squares before starting a new cycle with squares 97 to 100.
Identify the Highest Blue Square
From the complete cycles, the last square painted is the 96th square, which concludes the 16 cycles. The next square painted, which is the 97th square, starts a new cycle with a blue square. Therefore, the 97th square is also painted blue. Following this, the 100th square will be the first of the new green squares.
As a result, the highest numbered square that is painted blue is square number 97.