Question

Determine the 500th color shown when spinning a beach ball with six vertical sections colored white, orange, yellow, blue, red and green, starting with white.

Answer 1

To determine the 500th color shown when spinning a beach ball with six vertical sections colored white, orange, yellow, blue, red, and green, starting with white, we first identify the order of the colors and their positions. The sequence of colors in order is:

1. White
2. Orange
3. Yellow
4. Blue
5. Red
6. Green

Since the colors cycle through every 6 spins, we can find the color shown on the 500th spin by determining which position 500 corresponds to in this cycle.

To find the position, we need to calculate \( 500 \mod 6 \):

\[
500 \div 6 = 83 \quad \text{(whole part)} \quad \text{and} \quad 500 - (83 \times 6) = 500 - 498 = 2
\]

So, \( 500 \mod 6 = 2 \).

This means that the 500th color corresponds to the 2nd position in our color cycle.

Referring to our sequence of colors:
1. White (position 1)
2. Orange (position 2)
3. Yellow (position 3)
4. Blue (position 4)
5. Red (position 5)
6. Green (position 6)

Thus, the 500th color shown when spinning the beach ball is:

\[
\boxed{\text{Orange}}
\]