The Bulletin Board is located in your Home View below the Castle, in the centre right. The artwork shows an ornate public notice board with several postings pinned to it.
At random intervals of between 5 and 30 minutes, the Gift icon is displayed in a notification bubble above the board. This indicates that Lux has a Quiz question prepared for you, along with a guaranteed reward.
Whenever you are notified in this way, you should tap on the Bulletin Board and attempt to answer her question correctly. It costs nothing to try, and you will get a reward whether or not you find the correct answer. The loot consists of small quantities of resources, speed-ups or various forms of currency.
Excellent game mechanics