Wayside

A few years ago I revisited Louis Sachar's Sideways Arithmetic From Wayside School, a book with logic puzzles that while mystifying to me as a Grade 2 student, were now within my comprehension. Once you get the hang of them, the Sideways math problems can be solved on paper in a couple of minutes.

I thought it would be fun to write a program to generate more puzzles, and check my answers. This project is the result.

Apparently the Wayside books are still in print - consider buying one for the next generation of puzzle solvers!

Also, try out a Wayside browser game by Luca Masters: https://github.com/lkbm/sideways_math

How the puzzles work

The first puzzles in Sideways Arithmetic take the form of word-based addition:

   ELF
+  ELF
  ----
  FOOL

Each letter represents a digit between 0-9, and no two letters can be represented by the same digit. Can you deduce values for E, L, F, and O that would make the equation work?

Answer

E = 7
L = 2
F = 1
O = 4

   721
+  721
  ----
  1442

Later, Sachar extends the concept to multiplication. For example:

    SAY
x    SI
  -----
   NOSY
+  ICY
  -----
  ANNOY

Note that the script can solve both addition and multiplication puzzles, but currently only generates addition puzzles. A generated puzzle is guaranteed to have a unique solution - that is, each letter has exactly one possible value.

Usage

• Compile the program: ./build.sh
  • Requires JDK 17 or later
• Generate and solve puzzles: ./wayside.sh <arguments>

The puzzle generator uses a dictionary of 5000 common words that you can modify or replace to suit your needs. The dictionary came from a repo of public domain word lists.

Puzzle generator mode

Usage 1: Search for puzzles that sum to the given word.

Example: ./wayside.sh cheddar

Output:

 HYDRATE + DECLARE = CHEDDAR
 CARRIED + SACRED = CHEDDAR

Usage 2: Search for puzzles with the provided addend words.

Example: ./wayside.sh patrol trolls

Output:

PATROL + TROLLS = SPROUT

Puzzle solver mode

Usage 1: Solve a puzzle in the form:

   CANINE
+  FELINE
  -------
  BALANCE

Example: ./wayside.sh canine feline balance

Output:

A B C E F I L N
5 1 8 0 7 4 6 9

Usage 2: Solve a puzzle in the form:

    SAY
x    SI
  -----
   NOSY
+  ICY
  -----
  ANNOY

Example: ./wayside.sh say si nosy icy annoy

Output:

A C I N O S Y
1 4 9 2 8 3 5