Step by step
The question
Question: The pattern red, blue, green, red, blue, green, ...
keeps repeating.
What is the 50th color?
1 Find the block
The list starts again after green.
So the block that repeats is red, blue, green.
block = red, blue, green
The block is 3 long.
length = 3
2 Divide
The block comes again and again.
So we divide by its length.
What is left over tells us the place in the block.
n ÷ (length of the block): what is left = the place in the block
3 times 16 is 48.
So 16 full blocks take us to the 48th color.
50 minus 48 is 2 more.
50 ÷ 3 = 3 × 16 = 48, 50 − 48 = 2
3 Count into the block
Careful!
The 16 only counts full blocks.
The 2 left over gives the place.
Careful: not 16: the number of blocks ✗
2 left means place 2 in the block: blue.
50th color = place 2 in the block = blue
4 Check
Let's check by counting on.
A block ends at the 48th color.
Then we count on: red, blue.
The 50th is blue.
So it is right!
48th = green (end of a block), 49th = red, 50th = blue ✓
Let's look back.
First: find the block.
Then: divide.
Then: count into the block.
Last: check.
Answer
50th color = place 2 in the block = blue