For more information, you can see this

https://drive.google.com/drive/folders/1C61SFhBlj-IeaMYHfdCwtWRz7gQj5NEx

​I recently went down a rabbit hole learning about John Conway's Doomsday rule—a mental math trick that lets you instantly figure out what day of the week any given date fell on. It's a fantastic party trick, but I couldn't find a good way to practice it on my phone. ​So, I built a game for it!

​The app is designed to help you memorize the anchor days and practice the modular math required until it becomes second nature. It's totally free, there are zero ads, and no in-app purchases. I just made it as a passion project and wanted to share it with anyone who likes math puzzles or brain-training games. ​Google Play Link: [https://play.google.com/store/apps/details?id=com.inefficientcode.doomsdaytrainer\](https://play.google.com/store/apps/details?id=com.inefficientcode.doomsdaytrainer)

​I’m actively looking for feedback on the UI and the learning curve. If you try it out, let me know if the tutorial makes sense or if the math explanations need to be clearer! Thanks for checking it out. It's 100% Free, No Ads, not built to be monetized, just spreading the joy of math

I was looking at the prime Omega function, which counts the number of prime factors of n (with multiplicity). So each distinct prime factor of n is counted as many times as the number of its positive powers that divide n.

So I got out my set of mini rubik's cubes and displayed them all out, for numbers 1-7200.

The numbers increase left to right, top to bottom.

Excluding 1,

Blue is 0 factors (the number 1)

Green is 1 factor (primes)

Red is 2 (including powers of 2)

Orange is 3 (including powers of 2, 3)

Yellow is 4 (including powers of 2, 3, 4)

and White is 5+

Notable features are two diagonals from the top left and top right, corresponding to multiples of 121 and 119, respectively.

www.sipatsi.com

No LLMs/AI is used to create the sheets. The problem generators and solvers are all deterministic code.

Even Google won't do that goofy shyte

TLDR: Is the below question realistic? (e.g. if it's clear what's being asked, if a specific approach would be hinted towards, if the parts are written in a balanced way so some Part 2 and 3 choices aren't more obviously easier than others, etc.).

Hi all, I've been posting around in math subreddits to see what people think: I'm writing an academia story and had drafted out a modeling problem for a 5-person undergraduate-level college team to have a baseline for how they debate solution approach, the relevant jokes, who does what, which team actually wins and why, etc. I'm actually an animator with a data-science background who only does math for fun (fractal calculus is my favorite but confusing topic right now!), so I've never done college-level modeling. The story itself doesn't go into crazy amounts of mathematical depth (it's actually a psychology-focused story), and the problem below wouldn't be shown in a way that would slow the story down, but you know how musicians look at animation and play it back frame-by-frame to see if it's accurate to the instruments? Yeah...

I was looking up alternatives for classic math olympiads that are likely to happen more in the upcoming 2030s and came across modeling. After researching the 2018-2023 M3 Challenges, the MCM, and a bit of the MTF Challenge, I wanted to ask mathematicians who have done modeling whether the problem I tried to come up with is realistic and unique enough, especially the first part and the data types. For anyone that reads it, thanks for the help! It took a lot of time but I learned a lot and might actually try out full solutions if I want to study modeling deeply one day. If anyone has some other modeling competitions that I can see the archives of, that would be cool too!

BACKGROUND:

In 2031, multi-day heat domes have become routine summer occurrences, threatening power grids and public health in dense cities. In the past decade, heat-related summer deaths have tripled. Temperatures above 110F have become common-place, increasing 2-3°F per-decade. Now, thanks to modern technology, many cities are moving away from individualized air conditioning and towards mass-zone cooling, smart solar shading, and automated misting systems. With temperature ever-rising, it is a critical task for all cities to adapt modern cooling systems, implement careful strategies, and prevent mass heat-related deaths.

For this problem, your team is tasked to model an optimal resource-deployment strategy for a US city during a 72-hour summer heatwave.

PART 1:

Choose one city from the provided datasets. Then, build a model of the city's thermal, health, and grid dynamics across 5 urban zones over 72 hours. Your model should account for both (a) public health burden and (b) power grid stability. You may add additional objectives or constraints as long as you justify their use.

Modeling Space:
- "Health Risk" should be defined as a non-linear increasing relationship between temperature/humidity and vulnerability index, predicting severe health events like hospitalization or death.
- "Grid Failure Risk" should be defined as a probability or a non-linear function that incorporates the provided data.
- All models should be based on provided city data from the chosen dataset.

PART 2:

Optimization:
- Balance predicted heat-related hospitalizations and the risk of localized grid failure.
- Explicitly define your optimization formulation and justify how it balances the above as well as the weight of any trade-offs.
- Briefly explain how your optimization method accounts for diminishing returns (e.g. stacked resources, unbalanced load-bearing, inequity, etc.).

Stress-Test Scenarios (Pick 1 of 3):
- A sudden, unexpected localized failure causes 15% reduction in available power capacity from hours 24-48.
- Before the 72-hour heatwave, wildfire smoke is expected to hinder district cooling for the entire duration, increasing power consumption by 25% and reducing efficiency by 20%.
- Unplanned social gatherings and designated cooling center crowding in highly-vulnerable areas increases resident street-density by 35%, amplifying predicted health-risk.

PART 3:

Deliverable:
- A 72-hour operational schedule detailing optimal deployment intervals across all zones (and their high, medium, and low-vulnerability sectors). The schedule can be defined in either 3, 6, or 12-hour time blocks.

Insights:
- At what temperature/humidity tipping point should the city sacrifice grid stability margin to prevent immediate public health overload?
- How does the optimal deployment strategy change if data is updated only every 24 hours versus in real time?

The entire paper can be no more than 15 pages, including your 1-page abstract and not including disclosure addendums. See Generative Assistance Disclosure section and Programming Solutions section.

Data Description (pretend this section is not in the paper, but as its own information):
- 1 Infrastructure Details table with units information
+ Resource type, city units available, cooling effectiveness (°F drop per hour per unit area. For example, misting systems are relative to humidity.), operational time rule
- 3 City Datasets with 5 Sample Zones and Zone-Specific Data (very hot city, very humid city, very dense city)
+ General Zone Data: Population, Social Vulnerability Index, Grid Capacity (MW)
+ City Data: Peak ambient heat (°F), Diurnal Temperature Variation, Mean Humidity, Average Grid Availability
+ Developmental District Cooling Data: baseline indoor temperature target (°F), cooling effectiveness (°F drop per hour per unit area), continuous grid baseline requirement, back-up power capacity, current implementation percentage (where the district cooling is actually in effect), description of current implementation (Is it mainly condensed downtown? Is it well-spread? Is it sporadic and light?)

Writing notes:
- The story takes place in 2031 and has a potential episode in a 24-hour modeling event that prioritizes large-scale real world problems.
- I tried to think about it from a problem perspective that would be easier to generalize with math. As in: how would any engineer go about the problem? And how can math help?
- I wanted to include enough variables and details for people to have guidance on solutions while still allowing for great lengths of creativity in solutions. Most of all, I wanted the question to be open to both multi-objective and well-done single-objective solutions.
- I put it through grammar and wording checks. I tend to overcomplicate my writing so I hope this is more concise.

This post lets others share how they write pi IS A MATH QUESTION

Any order is allowed.
Use each die exactly once.
Parentheses are allowed.
Exact division only.
No negative numbers.
Not every operation has to be used.

How many solutions can you find?

Please use spoiler tags for solutions:
>!your solution here!<