Hi Toru, Do bear in mind that vocabulary.com defines English words in an informal way. When I use the web site, the informal language which they use usually makes it easier for me to understand the definition as it is crafted within a context or situation. They also try their best to explain any collocation that the word is used in. On the other hand, some of the sentences can appear quite convoluted to non-native learners of English. "Indulge" is often used with "in" or "on". Example: I will indulge (in) a cup of coffee now! I indulge myself (on) festive seasons. "Indulge" can also be used without "in" or "on". Example: I indulged him with a sumptuous dinner. (In this case, you allowed someone else to enjoy something that he or she likes.) In your sentence: "You can indulge (in) fantasies of figuring out the answer, or you can give in to an indulgent shrug and move on to another word." You can enjoy thinking of all kinds of definitions for the word. Alternatively, you can just shrug your shoulders* anytime you like and continue the same thing with another word. *We shrug our shoulders when we have no idea about something. Example: You are asked to guess the meaning of "adumbrate". You decide to be creative and and guess that the words means "to make someone dumb" since you could see the letters "d-u-m-b" in the word. Next, you decided to have fun by guessing that the word means "to explain something further" since "elaborate" also ends with the letters "r-a-t-e". Finally, you decided that you are tired of guessing, and shrug your shoulders and move on to the next word. Hope this helps. Cheers, Lance

to "indulge a fantasy" means to believe in something that is not realistic. you are 'indulging' yourself because it is not likely to be merited.