Logic grid puzzles (which include Sudoku puzzles and KenKen puzzles) are probably mostly encountered as “who-owns-the-zebra” type puzzles. The challenge of these popular puzzles is to ascertain certain facts and reach certain conclusions using deductive reasoning to process several statements. These deduction puzzles are the most basic logic puzzles and can be easily constructed with varying degrees of complexity to appeal to all levels of solving ability. By differing the number of elements, the amount of information given as well as the inter-connectivity of the defining statements (e.g., direct/loose association), these puzzles can be easy as pie or tough as nails.
Example: A Day at the Races
As an employee, Jack arrives at the racetrack to find three jockeys, Willie, Eddie, and Fidel, sitting in the media room waiting for a press conference to start. Jack’s boss (who loves puzzles) has left him a note instructing him to bring each jockey his racing silks and announce to the press which race each jockey has won and which horse he was riding. The challenge for Jack is that his boss’ note contains only six statements: Is it possible for Jack to know which jockey wore which silks, which race he won and which horse he was riding just by using deductive reasoning?
Create a Logic Grid
To begin, Jack draws a grid with four columns and four rows and then subdivides the lower three rows into three rows each as illustrated above (Fig 1). In the top row, he writes in the names of the jockeys in order (Willie, Eddie, Fidel) and puts the nine variables in the left-hand column. He then writes the six statements out below the grid. Note: The statements that refer to left and right are from the perspective of the viewer when looking at the jockeys at the press conference (in the grid). Now Jack reads each statement to see what conclusions he can come to for each one.
Willie has never won the Kentucky Derby.
This is a straightforward statement and allows Jack to eliminate one race option for Willie.
The jockey that rode Flash did not wear blue silks.
This statement doesn’t help until Jack knows either who rode Flash or who wore blue. He puts this aside for now.
The winner of the Belmont Stakes didn’t ride Zipper.
Once again Jack needs to know who won Belmont or rode Zipper before he can deduce anything from this statement.
The winner of the Preakness is to the right of Willie.
Now Jack can make some progress. He previously eliminated the Derby as an option for Willie and now he can eliminate the Preakness which means he can pencil in his first conclusion. Willie won the Belmont Stakes. Tada! Furthermore, he can eliminate Zipper as an option for Willie (see statement #3).
The jockey that rode Flash is seated to the left of the Derby winner.
From this statement, Jack eliminates Flash as an option for Fidel since he is seated on the far right. He now knows that either Willie or Eddie rode Flash.
The jockey that rode Zipper is seated to the left of the jockey who wore yellow.
This statement allows Jack to conclude that Eddie rode Zipper because the only other jockey who is to the left of anyone is Willie who Jack has previously concluded did not ride Zipper. Also, it follows that Fidel must have worn yellow and Willie must have ridden Flash. Now Jack returns to statement #2. From this statement, he can deduce that Willie must have worn red which means Eddie must have worn blue. And that completes the puzzle. Way to go, Jack!
How to Create a Logic Puzzle
As well as stating what value the characters have, mix in statements that say what a character does not have/do (“the sax player does not write ballads”) and/or that refer to the interrelationship of values and do not refer directly to the characters themselves (the R&B player sings jazz classics). Try to limit yourself to five or six statements. It’s a good idea to have someone test solve your puzzle for accuracy and fairness.
