The Sims 3 Logic Guide: The Smart Sim who can Teach, Win Chess and Solve Puzzles
This Sims 3 Guide was originally written for the PC and Mac versions of the game, but also will help owners of the console versions - PS3, Xbox 360 and Wii. Please remember some info or numbers may have changed.

Showtime Logic Addition - Dominioes
Playing dominoes (only with another Sim) on the new domino table will raise your Sim's logic skill. Unlike chess, this cannot be done solo.
Generations Logic Addition - Chemistry
I've uploaded a page about Chemistry, a new feature that came with The Sims 3 Generations. You can brew ten potion types, and this provides another route to maximizing logic. There's yet another logic skilll challenge that is covered on that page, which gives a 25% discount to the cost of making potions.
The Logic Skill is fairly unique in The Sims 3. The ways that you can make money with the skill are quite odd. Sims can earn money solving the unsolvable on the computer, finding new stars in the galaxy, and occasionaly by finding a meteorite that they spot falling from the sky. Sims with the Logic skill can also tutor and teach others their skills, making them useful friends or family to have around the neighborhood in the Sims 3.
Tutoring Children
At level 5 in logic, your Sim can tutor school-age children and help them raise the school performance bar, effectively raising their grade.
Making the Perfect Logic Sim
Traits that benefit Logic in the Sims 3
There aren't many traits that help with logic, but the few that do make a huge difference. First we of course have the Genius Trait, which increases the rate that Sims improve logic. They are also better at chess, and stand a greater chance at becoming a Chess Grand Master. Additionally, they can make money by solving the unsolvable on the computer.
Two other traits related to Logic are the Computer Whiz and Lucky traits. Lucky's role is simple, in that it will help your Sim to win more often when playing Chess. This is especially handy if you are pursuing the Chess Legend lifetime wish. Computer Whiz will allow your sim to play chess on the computer, but only with the more expensive computers.
How Best to Raise Logic in The Sims 3?
Take a Logic Class
A Logic class is offered at the Science Facility in town. You can only do it once, but it's a great way to gain the first level in logic.
Raising Logic
There are multiple ways to raise this skill and possibly earn money at the same time. The most raw is to go to the library and read a book on logic. This is good, but you could be earning money while raising logic at the same time!
Toddlers can raise Logic by reading the Counting for Those Who Cannot, Squares Are Not Triangles, and Being Smart For Fun and Profit Skill Books.
Solve the Unsolvable
With a computer, Sims can solve the unsolvable in the Sims 3. If they crack some really hard mathematical problem, your Sims can earn some free money doing this. At the same time, Logic will increase from the brain strain.
Search the Galaxy
There are two actions available to you with a telescope in the Sims 3 that can earn money for you. One is that you can search the galaxy (even during the day -- bug?) for stars and other objects. This requires level 3 logic. When your Sim discovers a celestial object, they can not only name it, but receive a tidy sum of cash for the find. It's not a lot of money, mind you, but you never know what your Sim will find in the vast expanses of space. Higher logic, and more discoveries leads to your Sims finding very profitable celestial bodies.
The other option is to look at the stars at night, which wlil raise your logic skill. Looking through the telescope, Sims in the Sims 3 can occasionally spot a meteorite crashing to the ground. They can then go to the map view to find the spot where it crashed, and collect it. The item can then be sold by dragging it to the simoleon icon on the inventory tab.
Playing Chess
Sims can satisfy the desire to raise logic, socialize, and have fun all at the same time by playing chess. Geniuses will enjoy this even more than other Sims, and can have a blast easily playing for a while. You'll also be able to challenge other players to a ranked game, by using the phone to 'Call', 'Invite over Ranked Chess Opponent'. Once the Sim is invited inside, you can then challenge them to a game of chess by clicking the chessboard.
Logic Challenges
Grand Master
Complete this challenge by making it to the fifth level by playing ranked players in Chess. Consider having high logic when you attempt this, as your Sim may have the wish to defeat several opponents in a row, granting you easy lifetime reward points.
Celestial Explorer
Upon discovering 20 stars, you'll complete this challenge. It allows your Sim to talk about their discoveries to other Sims. In my testing, I found this to be a better option than a regular chat, and it didn't seem to get boring. This reward is awesome, because you can easily befriend another Sim with long chats about your Sim's Astronomical discoveries.
Teacher Extraordinaire
You'll get this after twenty hours of tutoring a schoolage Sim. Your Sim will tutor Sims a bit faster once they've completed the challenge. Note that this feature is available at level 5, after which you can begin tutoring children, so if your Sim has kids, you can get started early!
Skill Professor
At level 10 in the logic skill, your Sim can teach other Sims the skills they know. At 30 hours completed teaching skills, this challenge is done, and will increase the rate at which your Sim teaches other Sims skills.
Opportunities
There are a easy opportunities to pursue based on the Logic skill. You can be tasked with participating in a study, searching the galaxy and even tutoring other Sims. Most of the Logic Opportunities are really easy to complete, and grant your Sim money and/or increases to the Logic skill. There's nothing too special here.
Logic-based Lifetime Wishes
The following Lifetime Wishes are strongly associated with the Logic skill:
Chess Legend: Become a Grand Master (Level 5) in Chess, and max the Logic skill.
Perfect Mind/Perfect Body: Master Athletics and Logic.
The Tinkerer: Master Logic and Handiness.
World-Reknowned Surgeon: Become a world-renowned surgeon by ascending to level 10 in the medical career.
International Super Spy: Take the Spy Career path of the Law career track to reach level 10 and become a Super Spy.
Forensic Specialist - Dynamic DNA Profiler: Take the Forensics career path of law to become a master DNA profiler.
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