Step 2: How it works
If you thought this, you would be right, but there is a way around this.
If you look at a 6 sided die, you might notice that there are never 2 dots that aren't diagonal or across from each other that are not there at the same time (except for the middle one). That means that we can connect the top left LED to the bottom right LED, the middle left LED to the middle right LED, and the bottom left LED to the top right LED.
So now we only need 4 pins to control all of the LEDs (the 3 pairs of LEDs and the single middle one). That means we have one pin left over to read the push button. Perfect!