From your perspective, what is the length of the red broomstick? From the perspective the observer riding the red broomstick, how long is your blue broomstick?

Each broomstick is equipped with a light on each of its ends. Observers that are riding the red broomstick flash both of its lights simultaneously, from their perspective. How far apart do you say the flashes took place?

You flash the lights on your blue broomstick simultaneously. According to those riding the red broomstick, how far apart did these flashes take place?

As the team of observers riding along with the red broomstick pass by you, they grab your blue broomstick in a manner that's simultaneous from their perspective. When they subsequently compare the length of the red and blue broomsticks, will they say that the blue one is longer than the red, shorter than red, or equal to red?

Going back to the original set up of the problem, with the blue broomstick at rest from your perspective and the red moving in the positive $x$-direction with speed $\frac{8}{17}c$, what speed must a third frame of reference have, from your perspective, in order that observers in this new frame claim that both broomsticks have the same length?