Lenny recently applied for an internship at Logicorp™, a company built around using logical reasoning to solve any sort of problems their clients face. The interview was long and difficult, and Lenny was asked many personal questions ranging from his favorite mathematician to his favorite color, and was given multiple logic tests. Considering that Lenny is a perfect logician, he aced the interview and was quickly offered a job. Today is his first day. After showing up to work bright and early, Lenny was given his first task: sorting paperwork.
Lenny’s manager handed him a box containing 9 folders of papers, corresponding to 9 of Lenny’s co-workers:
Aristotle, Boole, Cantor, DeMorgan, Euclid, Fourier, Gauss, Hopper, and Ockham. He handed Lenny a ream of nine colors of stickers:
Red, Orange, Yellow, Green, Blue, Purple, Black, White, and Gray. He asked Lenny to label each of the folders with a different color sticker. He then pointed Lenny to a set of three cabinets, each with three shelves, and instructed Lenny to file each of the folders into a different cabinet shelf. Before Lenny could protest that he did not know which color went with which file, nor where each file should go, his manager handed him a sheet of paper with the following instructions on it:
Each of the files must be labeled with a unique color and placed into a unique shelf, fulfilling the following requirements:
- Each cabinet1 should contain exactly one primary color2.
- Mr. Boole’s and Mr. DeMorgan’s files should be labeled with shades of gray3.
- The files labeled with the Red, White, and Blue stickers should belong to employees whose initials4 are alphabetically consecutive.
- Employees with a vowel initial should have files in the first cabinet.
- Files in the middle shelves should not be labeled with warm colors5.
- Employee’s files should not be labeled with colors that contain their initial (U.S. spelling).
- Colors formed by mixing two other colors must be filed adjacent6 to the colors that formed them7.
- The middle shelf of the middle cabinet should contain the files of an employee whose initial is one of the first five letters of the alphabet.
- Mr. Fourier’s file should not be placed in the bottom row.
- You should label the file in the bottom shelf of the third cabinet with your favorite color.
1 A cabinet is a single column of three shelves
2 The primary colors are red, blue, and yellow
3 The shades of gray are white, gray, and black
4 The employee’s initials are A, B, C, D, E, F, G, H, and O (they each have only one)
5 The warm colors are red, orange, and yellow
6 Orthogonally adjacent (above or below in the same cabinet / to the right or left in the same row)
7 Red and blue mix to form purple; red and yellow to form orange; yellow and blue to form green; black and white to form gray. Assume no other colors can be formed by mixing
Lenny understood that this was a test of his logical wit. After studying the rules and making a few important deductions, he confidently placed a single sticker on each folder, filed each folder into a separate shelf, and returned to his manager. His manager was quite impressed that Lenny had correctly deduced the correct pairings of files, colors, and locations without any guesswork.
Now it’s your turn to apply for Logicorp™. Can you figure out how to file everything? Remember: There is only one solution, which Lenny was able to reach through pure logical deduction.
Answers should show the color corresponding to each employee’s file and where that file goes, along with the logical steps one took to come to that conclusion.