I agree, this puzzle was a huge pain when I did it too. You just need to try to work out the combinations with whatever pieces you already have.
For the first slot, you'll need a yellow triangle (9). For the second slot, you can use a yellow square (12) and a red triangle (3) and for the third slot, you can use a blue square (20), an orange triangle (6), and an orange circle (2), all of which you have. You just need the yellow triangle so set the other pieces that you need aside and try to get one with the exchanger. You can also talk to the gnome for extra pieces. Hope this helps