# Circle, circle + triangle, ... sequence of groups of colored shapes:

I can't seem to find a logical consistency for the answers. What is the correct answer?

• I hate these kinds of questions myself—it could literally be anything. There are an infinite number of continuations of any sequence. These are really “guess what I (the problem creator) am thinking” questions. It’s
– bob
Jul 12, 2023 at 19:56

Because

Each step is made of 2 items: one old + one new. We have exactly one occurrence of previous step's new item, and a new item appears - its occurence increases with the step number

As a summary, if we except step 1 we have

Step 2: 1 red circle + 1 new item: triangle
Step 3: 1 triangle + 2 new items: blue square
Step 4: 1 blue square + 3 new items: stars
Step 5: 1 star + 4 new items: purple square
Step 6: 1 purple square + 5 new items: blue circle

To follow completely this rule, I would have started with

empty cell: 1 occurrence of previous item (does not exist) + 0 occurrence of new item (red circle)

• I think the start is exactly right: 1 occurrence of previous item does not exist, so you only have 1 new item: the red circle. You start counting with 1. Jul 12, 2023 at 11:10
• @Lezzup the new items should occur 0 times for this first step, am I wrong? Jul 12, 2023 at 11:26
• Nope, you're right. Indeed, at step n you should get n-1 new items. I was squint looking :) Jul 12, 2023 at 11:55