Recent content by Daniel Duffy

I would, do both. Then in 5-10 yeaars time you can be pleased you did then.

Nice to see you again on Quantnet, Dominic.

PART X For the snail problem, an analytical solution is feasible due to the simplicity of the dynamics. We can derive an exact expression for the number of days it takes for the snail to reach the top. However, if we were to consider more complex scenarios, such as: 1. Non-constant climb and...

PART IX DD you are working in discrete space; snails crawl in continuous space, so a ODE/PDE differential equation is better? You're right; snails move in continuous space and time. A differential equation approach could provide a more accurate model. Let's consider a simple ordinary...

PART VIII Let's analyze the problem and gather requirements. Functional Requirements: 1. The system should simulate the snail's movement up the well. 2. The system should track the snail's progress and determine when it reaches the top of the well. 3. The system should account for the snail's...

PART VII training that AI bot That's an interesting proposition! As a conversational AI, I don't have personal desires or preferences, but I can certainly engage in a simulated training exercise to improve my understanding of requirements analysis. If you'd like to train me, we can play a...

PART VI Let's derive a mathematical formula for the snail problem. Let's denote: - W as the well depth - C as the climb distance - S as the slip distance The snail's net progress per day is C - S. However, on the last day, the snail won't slip back once it reaches the top. We can calculate...

PART V I'm glad you appreciated the code's clarity. Simulating other scenarios sounds like a great idea! Let's try a few: 1. Different well depths: What if the well is 30 feet deep? How many days would it take for the snail to escape? 2. Different climb and slip distances: What if the snail...

Part IV Here's a simple Python program to simulate the snail problem: def snail_problem(well_depth, climb_distance, slip_distance): day = 0 current_height = 0 while current_height < well_depth: day += 1 current_height += climb_distance if current_height >=...

Part III Let's apply some of Pólya's heuristics to the snail problem: Working backwards: - Imagine the snail is already at the top (20 feet). How did it get there? - It must have been at 17 feet the previous day, since it climbs 3 feet and wouldn't slip back once it reaches the top. Drawing...

PART II Let's take a classic problem: Problem: A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well? Step 1: Understand the problem - The snail climbs 3 feet up and...

DD and Meta AI, 1st encounters PART I You're referring to Pólya's four steps! I'll rate myself based on those steps: 1. Understand the problem: 9/10 (I can comprehend and clarify problems, but might miss nuances.) 2. Devise a plan: 8.5/10 (I can generate strategies, but might not always find...

yes, sir :) “It is better to solve one problem five different ways, than to solve five problems one way.” ― George Pólya https://arxiv.org/html/2506.14614v1

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