appleby / arithmetic-meme

Solutions to a simple arithmetic puzzle

arithmetic-meme

This repo contains a solution in prolog to a simple arithmetic puzzle that went viral-enough on the internet that it popped up on reddit or hackernews or somewhere.

This puzzle seemed like the perfect excuse to write my first Prolog program.

Problem statement

Here are the relevant bits of the problem statement, copy/pasted from here.

All you need to do is place the digits from 1 to 9 in the the grid. Easy, right?

...

You need to fill in the gaps with the digits from 1 to 9 so that the equation makes sense, following the order of operations - multiply first, then division, addition and subtraction last.

Running the code

Example SWI-Prolog session

?- [solve].
true.

?- run_tests.
% PL-Unit: solve ................................................................................................................................................................................................................................................................................................ done
% All 288 tests passed
true.

?- solutions(X).
X = [3, 9, 2, 8, 1, 5, 6, 7, 4] ;
X = [3, 9, 2, 8, 1, 5, 7, 6, 4] ;
X = [8, 9, 2, 3, 1, 5, 6, 7, 4] ;
X = [8, 9, 2, 3, 1, 5, 7, 6, 4] .

Example lisp session

CL-USER> (load "solve")
T
CL-USER> (run-tests)
T
CL-USER> (solve)
...list of solutions...

Runtime comparisons

Here is a table showing the runtimes of the various solutions when run on my aging laptop. They range from "pretty fast" when using the clpfd library on SICStus to "dog slow" when using the clpq library on SWI Prolog. In fairness, part of the reason the SWI Prolog solutions are slow is that I still have no idea how to write Prolog.

variant (time units are seconds)	SWI Prolog	SICStus
normal_precedence_constraint_clpfd	6.236	0.150
linear_precedence_constraint_clpfd	3.360	0.060
normal_precedence_constraint_clpq	62.731	12.230
linear_precedence_constraint_clpq	63.987	12.690

This repo also contains a reference solution in lisp. The lisp solution is a brute-force search over the 9! possible input permutations, and makes no attempt to be fast.

variant (time units are seconds)	SBCL	CLISP	CCL
normal-precedence-constraint-satisfied-p	0.596	2.12	0.977
linear-precedence-constraint-satisfied-p	0.722	3.13	1.217