Give light to 1 / 4 LED's random order

Hi. I was wondering if anyone could help making a code for a game.
I have 4 buttons with LED's which I want to be powered randomly.

To start the "game" you have to press one of the four buttons twice. After some seconds one of the four buttons will light up and you have to press the button which lights up. When you press the button which lights up, it turns off. This goes forever until you press a button twice.

Is it possible to add a speed effect, so the lights will be powered faster as you get into the game?

Thank you

It's all possible. Just a matter of programming.

And of course we like to help. But for now, I see nothing to help with, just a program request. For that we have a separate section where you can pay somebody. If you really want help, start posting what you tried and where you're stuck which includes code and a schematic (NO Fritzing).

Your speed idea doesn't make sense. Who cares about how soon the next light turns on? You probably mean a window of time to press the button once lit before a loss condition.