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Source: https://writers.stackexchange.com/a/37272
License name: CC BY-SA 3.0
License URL: https://creativecommons.org/licenses/by-sa/3.0/

The other answers here are all to do with making the character come across as intelligent in **conversation**. There is a flip-side to this, which probably bears mention: Non-verbal cues. Consider the following scene:

> Protagonist **_A_** is waiting for Character **_B_** in a café, reading a newspaper to pass the time. When **_B_** arrives, **_A_** folds the newspaper, places it on the table, and starts the conversation. After a couple of minutes, socially-inept **_C_** suddenly bounds up and starts chatting away at **_A_** , completely ignoring **_B_**.
> 
> By the time **_A_** finally extricates themself from the (rather one-sided) verbal deluge, they notice that **_B_** has passed the time by getting out a pencil and working through the one of the harder logic-puzzles (sudoku, nonogram, etc) in the newspaper with remarkable efficiency.

This, of course, only works for certain expressions of intelligence - for a musical prodigy or a skilled tailor you would need a differenct scenario - but it's like this: If you want to indicate that someone is a mechanical genius, do you have them talk about sprocket design, escapement mechanism and gear ratios, or do you have them casually strip down, repair and rebuild a broken clock with little more than a glasses-repair kit and a swiss-army knife?

Original score: 5