I don't have a game save from right after that puzzle, but I can tell you what would make it easy.
Draw a star map on paper. When the first star lights up, mark that #1 on your map. Then click on that star in the game.
Next, that star will light up plus one more new one. Mark that one down on your star map as #2, then click the first and second stars in the game.
Next, the #1 star will light up, then the #2 star will light up, then a new star will light up. Mark that one down as #3 on your star map on paper.
Continue on marking each new star on your map on paper, through #12 I think it was, and clicking them in sequence in the game. There's no time limit and the game will wait on you while you mark numbers on your piece of paper.
That's how I got through it and had no problems with it. Good Luck!
