Visual Thinking Research

At first, we tried this puzzle: Identify two identical umbrellas which can be rotated.

First, we just looked at the darkest color of 4 different colors, and did grouping the similar structures of the color. However, we then realized those can be rotated.  Those grouping are so messy and bothering finding out the identical ones from there. 

We started as different way...

Actually, we a kind of noticed what it is going on here. The combination of outside color and inside color should be very important. So, we tried grouping the same combinations such as white id outside, and gray is inside (The real puzzle shown in monitor was vivid color, but this is printed.) Then, after grouping, we looked at the other combinations next to what we just classified. Thus, we got it!! This is the best way to find out. 

Next puzzle is... Which of these windows can be drawn by one line. 

 

This is my attempt, simply done. I tried taking a pencil on the center edge at first. But, every time I tried, it failed. Then, I started the points on crossing line. It should be a common way to solve. 

Finally, this is done by my friend. She is clever since she at first take a pencil on line of the center objects. If they are not touching the outside line, it won't be done. Or, if there are no objects. So, I think it is the best way for this puzzle.