deduction
Using facts and logic to figure something out.
Deduction means reaching a conclusion by using logic and known facts. When you figure something out through careful reasoning rather than guessing, you're using deduction.
Sherlock Holmes became famous for his brilliant deductions. He would observe that someone's shoes were muddy, their umbrella was wet, and their newspaper was from a morning edition, then deduce that they had walked to work that morning in the rain. Each clue pointed logically to the conclusion.
You use deduction all the time without realizing it. If you come home and see cookie crumbs on the table, an empty milk glass, and your sister looking guilty, you might deduce that she just had a snack. In math, when you know that all squares have four equal sides, and you're told a shape is a square, you can deduce it has four equal sides. That's deduction: starting with what you know for certain and reasoning your way to what must be true.
The word also means subtracting an amount from a total. When stores offer a deduction of ten dollars off your purchase, they're subtracting that amount from what you owe. Your parents might get a tax deduction for charitable donations, meaning that amount gets subtracted from their taxable income.