Really hard interview question about rebuilding a picture. What approach would you use for this question?

You might not get the same picture next time, but if you do I would say, "Draw a square and then draw a diagonal line from the top left corner to bottom right corner." "then draw a line from the bottom left corner to that line, so the bottom left side looks like it is two triangles." "Now in the right top corner, make an equilateral triangle, the corner is one point and the two other points are half-way down the right side and half way across the top side." "so, now, there should be a diagonal empty space between the three triangles we see now." "Color the top right triangle Yellow, Color the bottom triangle Green and color the left Triangle Orange." "Now draw a line from the mid-corner of the orange triangle to the middle of the bottom line of the yellow triangle and them make that a square that fits on the top Orange Triangle line". "Color the square aqua." "There should now be an empty triangle space between yellow and Orange Triangle. Color that triangle space purple" "Now draw a line from the middle of the yellow triangle to the middle of the Green triangle's right line." "That should leave a triangle space to it's left and a parallelogram on the right. Color the new triangle Blue and the Parallelogram Pink."

DONE.

You could also have the shapes made in different orders, but I would use the shapes and positions of lines to explain.

I would say put the biggest pieces in the bottom first then do the triangle on top put the square in place place the triangle next to it then place the other two where they fit. not sure if the blue and purple triangles are the same size or not.

Arrange the shapes by size and have the other person do the same. then have them work down the line.