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So what I did here was at first I tried to arrange it systematically like: same vegetables first and then changed to another one and I only got 10 sauces.
I tried to note down the first order and then rearranged its, and I concluded that you need to arrange in order to get more than 3 couples of 2 layer sauces. So yeah, basically just mess with it for a few minutes and you'll find out.
Btw this is my sample: 
(L = lecture, O = onion, T = Tomato, \ = sauce) 
L \\ O \ O \\ T \ T \ T \\ L \ L\\ O