Advent of Code 2024 Day 13 (BaseA Style)

[AlteryxCommunityTeam]

Discussion thread for day 13 of the Advent of Code - https://adventofcode.com/2024/day/13

[CoG]

Nice! Lucked out with another easy problem. Having a mathematics background was very helpful.

Spoiler

In order to identify whether a particular prize is achievable, it helps to recognize that we have 2 variables at our disposal (1) 'A' button presses and (2) 'B' button presses and two outputs to achieve (1) Px and (2) Py (aka the X and Y positions of the Prize). This sets up a linear system of equations, and if you know anything about linear systems, then you know that when the count of variables and outputs are equal, then there is at most 1 solution (assuming the equations are not multiples of one another, which is true for the problem data) 

Thus, the solution to this problem is to identify all integer solutions to the provided systems of linear equations. If one exists, then that is the only solution, and thus, by extension, the minimum solution as well. Perform the strange cost calculation (which tripped me up initially; reading is still important apparently). Sum up all the costs and solve the problem. Thankfully, part 2 still fits an int64, so no challenge there at all!

[gawa]

DO THE MATH!😁

Using a pencil and paper is not violation to Base-A, I believe.

Spoiler

Part1: Calculate all patterns and find the match result
Part2: Gave up the approach in part1. After 5 minutes, I realized this is just a simple algebra that has restriction of 'answer is integer'.

[ScottLewis]

Came here all excited to write about Math but @CoG beat me to it. 

I will accept the consolation prize of a substantial amount of bonus sleep.

[AkimasaKajitani]

Solved!

Make Column tool is useful for dataprep.

Spoiler

I solved a system of simultaneous equations. I thought there was some trick to Part 2, but it was none!

[abe_ibanez]

I was stuck on this for 40 minutes until the solution finally hit me. Once I figured out the way to solve it, it only took a few minutes. Really fun problem though. 

Spoiler

[kelsey_kincaid]

This one was fun! 

Spoiler

It took me longer to conceptualize the math than to build the workflow. I had to bust out a pen and paper to get the systems of equations right in the formula tool. Part 2 came very easily once Part 1 was built.

[Raj]

Both methods added 
brutal did not work for part2

[Qiu]

I took the easy way. 

Spoiler

[DaisukeTsuchiya]

P1 was solvable with brute force, but P2 didn’t work out.

Spoiler

I used the system of equations formula:
For Ax+By=C　Dx+Ey=F then x=(BF-EC) / (BD - EA), y=(FA-CD) / (AE - BD)