My brain wasn't working and I couldn't figure out the math, so I had to simplify my design. It finishes 10.25-inches square.
The requirements were: a square 10 x 10 inches (up to 16 x 16 inches) using pool blue, lime green, orange, light pink, berry pink, and/or plum purple.
I used Kona School Bus, Limelight, and Geranium. I matched the thread in the orange triangles and and reversed the colours in the four corners.
I have no expectation of my project being selected, but I wanted to play along with the challenge. It's nothing fancy, but I'm happy with what I accomplished in a couple of hours.
I am not a fan of hand sewing, but I have to say that I really like a faced binding on small projects. This is the tutorial that I use.