What kind of study design is this and what kind of statistical analysis should be suitable? I plan to conduct a study in which respondents will be asked to solve total 6 puzzles together.
Is there a specific study design (name) for this?
The scenario would be:

*

*First, user A will use a mobile device and user B will use a computer to solve puzzle 1, 2, and 3 together.

*Then they switch roles: user A uses a computer and user B uses a mobile phone to complete puzzle 4, 5, and 6.

Then we repeat for the next users.
The goal is to evaluate the user performance and satisfaction and determine if mobile phone or PC were better.
I reckon it is a two-factor: device type (mobile and computer) and puzzle (1, 2, 3, 4, 5, 6 puzzles) within-subjects experimental design.
In that case can I use Oneway ANOVA for this?
Thanks in advance.

This sounds very much like a stepped-wedge trial - an improvement to a classic RCT as it is designed to remove bias. In this scenario, each group receives both the control and the treatment condition and by the end of the trial, both between and within-cluster comparisons are possible, increasing power and the potential for analytic insights.
You can analyze the results with Linear Mixed Models (LLM), Generalized Linear Mixed  Models (GLMM) or Generalized Estimating Equations (GEE).
The first international conference on this topic was held in the US in 2016 and written about in BMC: https://www.biomedcentral.com/collections/SteppedWedge
