A total of 180 marbles (gray, white, and black) are placed in a line. If the first five are gray, followed by four, followed by three black, followed by five gray, followed by four white, followed by three black,... If this pattern continues, what is the color of the 158th marble in this line?

Well, I hope the marbles weren't playing a game of hide and seek while you were counting them! Alright, let's do some funny math here.

If we look closely, we can see that the pattern repeats after every 16 marbles. So, to find the color of the 158th marble, we can divide 158 by 16 and see what the remainder is.

158 divided by 16 is 9 remainder 14.

Now, let's break it down:
- The first five marbles are gray.
- From marble number 6 to 9, we have four black marbles.
- From marble number 10 to 14, we have five gray marbles.
- From marble number 15 to 18, we have four white marbles.
- From marble number 19 to 22, we have three black marbles.

So, based on our calculations, the 158th marble will be the 14th in the pattern, which is a gray marble. Congrats, you've reached the gray zone!

To determine the color of the 158th marble in this line, we first need to analyze the pattern it follows.

From the given information, we can observe that the pattern repeats after every 16 marbles. In each repetition, there are 5 gray marbles followed by 4 black marbles followed by 5 gray marbles followed by 4 white marbles followed by 3 black marbles.

To find the color of the 158th marble, we need to determine which portion of the pattern it falls into.

The number of complete repetitions that have passed can be calculated by dividing the marble number by 16:
158 ÷ 16 = 9 (with a remainder of 14)

This indicates that the 158th marble is within the 9th repetition, as there are 9 complete repetitions of the pattern.

Since each repetition consists of 5 + 4 + 5 + 4 + 3 = 21 marbles, the first 9 repetitions would account for 9 × 21 = 189 marbles.

However, we are only interested in the 14 marbles (remainder) after the 9th repetition.

Analyzing these 14 marbles, we find that they follow the pattern: 5 gray, 4 white, 3 black, 2 gray.

We can conclude that the 158th marble is the 2nd gray marble within the 14 marbles after the 9th repetition.

Therefore, the color of the 158th marble in this line is gray.

Did you leave out the word "white" after the first word "four" ?

Note that after each twelve marbles, the cycle repeats. Therefore after 156 (12x13) , #157 will be the samd as #1 etc.

To find the color of the 158th marble, we need to analyze the pattern.

We see that the pattern repeats every 14 marbles: 5 gray, 4 black, 5 gray, 4 white, 3 black.

Since 158 is not divisible by 14, we need to find the remainder when 158 is divided by 14.

158 ÷ 14 = 11 remainder 4

This means that the 158th marble is in the same position as the 4th marble in the pattern.

The pattern starts with 5 gray marbles, followed by 4 black marbles. Therefore, the 4th marble in the pattern is a black marble.

Therefore, the color of the 158th marble is black.