Cogitème’s logic games

round the circle, roundabout
Roundabouts
straight in the row, row
Rows
championship
Championships
logic system
Logic Systems

Solved examples

Logic Systems

Five friends are going shopping on Black Friday, the day after Thanksgiving. They each purchase different items whose prices have all been reduced by a different percentage.
(1) Gary got 40% off.
(2) Gary did not buy a computer.
(3) Bob bought a movie.
(4) Jen did not buy a computer.
(5) Jen got 35% off.
(6) The television had a 60% markdown.
(7) Barb did not get 55% off.
(8) The computer did not have a 20% markdown.
(9) The CD did not have a 35% markdown.



Step 1:

You know that Gary got 40% off (1), that Jen got 35% off (5), and that Bob bought a movie (3), so you can begin by putting this information into three of the spots.
Gary Item 40%
Jen Item 35%
Bob movie Markdown
Person Item Markdown
Person Item Markdown

Step 2:

You also know that the television had a 60% markdown (6). Since you know that neither Gary nor Jen bought a television since they did not get 60% off (step 1) and that Bob did not buy a television (3), you can fill in this information in one of the remaining two spots.
Gary Item 40%
Jen Item 35%
Bob movie Markdown
Person television 60%
Person Item Markdown

Step 3:

You know that neither Gary (2) nor Jen (4) bought a computer. Since the other two spaces are for the Movie and the Television, you can put the Computer in the last space.
Gary Item 40%
Jen Item 35%
Bob movie Markdown
Person television 60%
Person computer Markdown

Step 4:

The computer did not have a 20% markdown (8), since there are only two possible markdowns left (20% or 55%), you know that the computer must have had a 55% markdown. Therefore, the movie must have had a 20% markdown.
Gary Item 40%
Jen Item 35%
Bob movie 20%
Person television 60%
Person computer 55%

Step 5:

Since Barb did not get 55% off (7), she could not have bought the computer. There is only one other spot left, so Barb must have bought the television.
Gary Item 40%
Jen Item 35%
Bob movie 20%
Barb television 60%
Person computer 55%

Step 6:

There is one person and one item that you weren’t given any information about. Since all of the other names have been used, you know that Amanda must have bought the computer.
Gary Item 40%
Jen Item 35%
Bob movie 20%
Barb television 60%
Amanda computer 55%

Step 7:

Since the CD didn’t have a 35% markdown (9), Gary must have bought the CD for 40% less. Therefore, Jen must have bought the last remaining item, the videogame.
Gary CD 40%
Jen videogame 35%
Bob movie 20%
Barb television 60%
Amanda computer 55%