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

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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!

Main.yxmd

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'.

2024D13_gawa.yxzp

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!

Day13.yxzp

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

day13solution.yxmd

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.

2024_Day13_KelseyKincaid.yxzp

Raj

Both methods added
brutal did not work for part2

Aoc D13.yxzp

Qiu

I took the easy way.

Spoiler

AOC2024-Day13.yxmd

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)

スクリーンショット 2024-12-13 185446.png

DT2024_Day13_Rev0.yxmd

DataNath

Day 13 done and dusted! I've always struggled with Maths so did have to look up formulae etc, but converted this into BaseA myself. If nothing else this has been a great refresher/lesson in linear equations!

Spoiler

leozhang2work

Spoiler

Initially thought finally a problem for Optimization tool, even the location optimizer macro. After some unnecessary fiddling, back to basic linear algebra 101 😂

day 13.yxmd

cgoodman

@leozhang2work here's how to solve it with the optimisation macro, which I will still count as BaseA as it's a tool installed with Designer 🙄

Spoiler

Part A: Took the brute force approach to solve the equations by generating the rows, but this approach is tool slow for part B
Part B: I knew I could solve it using the optimisation tool, I just need to work out how to shape the data so it would work for the inputs. I've always struggled to know how to do this as I've previously reverted to using manual inputs into the tool but find this is higher risk of typos, plus for today I needed to find a method which would wrap this inside a batch macro.

Screenshot 2024-12-13 111648.png

Day13Batch.yxmc

2024_AoC_ChrisGoodman_Day_13.yxmd

Goddenra

If only I'd taken a step back at the start and realised it's just maths!

Day13.yxmd

Spainey

It took me a while to realise how easy this one actually is 😂

After generating 100 rows each for the button a presses and 100 rows for the button b presses and trying each combination to see which ones worked. I realised that these linear equations can be made much simpler to remove the reliance on Generate Rows.

Spoiler

I kept the Generate Rows method in for Part 1, creating a Bool flag to tell me which equations resulted in correct answers:

([A_x] * a) + ([B_x] * b) = [P_x] && ([A_y] * a) + ([B_y] * [b]) = [P_y]&#8203;

and then filtered out where this was false, before calculating the tokens and aggregating:

[a] * 3 + [b] * 1

For Part 2, I went off in completely the wrong way when I tried to make the X equation and Y equation equal when I multiplied the A and B coordinates by the Prize coordinates. So I got the pen and paper out and worked it out properly and adjusted my formulae.

// solving for a, multiply prize by b
p_diff = abs(([P_x] * [B_y]) - ([P_y] * [B_x]))

// solving for a, multiply a by b
a_diff = abs(([A_x] * [B_y]) - ([A_y] * [B_x]))

// validate the modulo
Valid Multiple = MOD([p_diff], [a_diff]) = 0

// Calculate a
IF [Valid Multiple] 
THEN [p_diff] / [a_diff]
ELSE NULL()
ENDIF

// Calculate b - watch out for edge cases that don't go into the remainder an equal number of times
IF !IsNull([a]) && MOD(([P_x] - ([A_x] * a)), [B_x]) = 0
THEN ([P_x] - ([A_x] * a)) / [B_x]
ELSE NULL()
ENDIF

2024_AoC_mark-spain_Day_13.yxmd

Yoshiro_Fujimori

My solution.

Spoiler

Workflow

Formula
[A] = ([M22]*[X] - [M12]*[Y]) / ([M11]*[M22] - [M12]*[M21])
[B] = ([M11]*[Y] - [M21]*[X]) / ([M11]*[M22] - [M12]*[M21])

workflow.yxmd

Blake_E

really dusting off the cobwebs in my brain on the math for this one. thanks Khan Academy for the refresher!

Spoiler

Day13.yxmd

mmontgomery

Day 13. More in spoiler

Spoiler

P1: Brute force
P2: System of equations by hand then converted it to Alteryx workflow.
94x1+22x2=8400;
34y1+67y2=5400

x1=y1
x2=y2

94y1+22y2=8400
34y1+67y2=5400

67(94y1+22y2=8400)
22(34y1+67y2=5400)

629841y1+1474y2=562800
-(748y1+1474y2)=118800

5500y1=444000
y1=80
y2=40

Rinse repeat

Day 13_MM.yxzp

Hub119

Finally getting around to posting this today... took the optimization approach (without using the R tools) to part 1, and then got out the old pen and paper to do some quick math to sort out my formulas for part 2 so my computer wouldn't explode on me... We've passed the halfway mark... no going back now.

Spoiler

AoC 2024 Day 13.yxzp

geoff_zath

Spoiler

AoC_2024_day13_v2.yxzp

ccanterman

Solved. "Just" Algebra and systems of equations.

I used pen and paper first to get my systems of equations sorted out and then did the Alteryx build

Spoiler

Stationary picked up at Inspire 2024:

Solved.

math problem.😁

Excited to have an easy solve...

Spoiler

... once I remembered the equations to solve linear equations

Good thing is though I recognised what I needed to do today. Brain is on the mend.

Due to using 24.2, I can just have a single tool being my "switch" between Star 1 & 2. Just turn off the equations in the formula tool

Day 13 - Both Stars.png

I know I can solve this in a more succinct way too, just need to catch up massively at the moment.

Samantha_Cllifton_Day13.yxmd

estherb47

Easy in concept, but took me a while to figure out the math needed

Spoiler

Might be the fewest tools I've ever used in Advent of Code

Found it very interesting that Alteryx found solutions, even when there wasn't a real one. So, had to add in a validity checker.

lwolfie

Once I brushed off my math skills, it was a lot faster.

Day13.yxmd

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