Solutions to the 24 puzzle

The 24 puzzle asks Given the numbers A, B, C, and D, is there a way to combine the numbers using arithmetical operations +,-,*, and / so that the whole equation evaluates to 24? I got curious about what inputs to the 24 puzzle had a solution and what ones did not. So I wrote a 24 puzzle generator and a 24 puzzle solver. I also wrote the following shell script (not a joke, I actually wrote this command line):

python3 genall.py | while read; do (echo $REPLY; (echo 4; read; echo $REPLY; read; echo $REPLY; read; echo $REPLY; read; echo $REPLY) | python3 24.py) | xargs echo ; done | tee rawoutput.txt | python3 filer.py

After all that, I had web pages for every solution to the 24 problem. So I have linked all of these web pages below on the off chance that anyone else thinks this is interesting. The raw output is also available if you want to grep it and explore for patterns.

As a brief show of what can be done, here are the hardest small problem instances according a very simple heuristic:

$ grep '.*/.*/.*' rawoutput.txt | grep -v '[0-9][0-9]' | awk '{ print $1 " " $2 " " $3 " " $4 }'
1 3 4 6
1 4 5 6
1 6 6 8
3 3 8 8

Some of the solutions to those four problems seemed so strange that I had to verify them by hand. Another fun fact is that 6,934 out of 17,550 problems have no solution, so if you pick 4 numbers between 1 and 24 (inclusive) at random, you have a greater than 1 in 3 chance of having an unsolvable problem!

Enjoy! Please let me know if you find this useful or interesting, and especially if you do anything fun with it :)

—Peter Boothe <peter.boothe@manhattan.edu>