What I assume is that all of the "secret" combinations work from day one. It's just each day a new one will be revealed via fireworks. These are two I've discovered myself:

3 Hi-Potions of Intelligence
- 1x Colored
- 3x Green
- 2x Purple


Odd Egg (no need to have a hat in inventory)
- 1x Painted
- 1x Red
- 2x Blue
- 1x Green
- 1x Yellow