Solving Homework Problems, Puzzles, Competition Problems, Olympiad Problems with ChatGPT and Computation

Over the past few weeks, I have been accumulating a variety of math problems from resources such as Mathematics Magazine, Crux Mathematicorum, American Mathematical Monthly, universirty Mathematics competitions, National Mathematics Olympiads, and more. I have been experimenting with these problems in ChatGPT with the Wolfram Plugin and successfully solving a good fraction of them. I kept the ones that ChatGPT with the Wolfram plugin could solve in a notebook.
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Recently, ChatGPT introduced a bookmarking feature for sessions. This greatly simplifies the process of sharing a chat, rendering screenshot-taking redundant.
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Also recently I got some access to the Code Interpreter version of ChatGPT. I found this intriguing and decided to test the same problems on this platform as well.
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Code Interpreter ChatGPT succeeded in about 50% of the problems.
The links to both the Wolfram Plugin chat sessions and the Code Interpreter chat sessions can be found below and show the approaches used and the code executed..
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In cases where the Code Interpreter successfully solved a problem, I compared the length of the actual code (including comments for simplicity). On average, the Wolfram Language code was roughly 27% the size of the Code Interpreter’s Python code.
Out[]=
Wolfram Plugin
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Code Interpreter
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Proving Trigonometric Relation
✓
Proving Trigonometric Relation
□
Divisible Two-Digit Integers
✓
Divisible Two-Digit Integers
✓
Summing Series of Integers
✓
Summing Series of Integers
×
Finding Quadratic Equation Parameter
✓
Finding Quadratic Equation Parameter
✓
Determining Anne and Tom’s Ages
✓
Determining Anne and Tom’s Ages
×
Sock Color Probability Solutions
✓
Sock Color Probability Solutions
✓
Cone Dimensions Calculation
✓
Cone Dimensions Calculation
×
Arranging Integers with Constraints
✓
Arranging Integers with Constraints
✓
Computing Limit of Expression
✓
Computing Limit of Expression
×
Solving Average Number Problem
✓
Solving Average Number Problem
✓
Intersecting Circles Distance Calculation
✓
Intersecting Circles Distance Calculation
×
Ladder Height Against Wall
✓
Ladder Height Against Wall
□
Solving Nonlinear Equation System
✓
Solving Nonlinear Equation System
✓
Finding Specific 5-Digit Number
✓
Finding Specific 5-Digit Number
✓
Maximizing Trigonometric Function Value
✓
Maximizing Trigonometric Function Value
□
Polynomial Equation Solutions Count
✓
Polynomial Equation Solutions Count
✓
Maximizing Distinct Pairwise Sums
✓
Maximizing Distinct Pairwise Sums
✓
Nth Derivative at Zero
✓
Nth Derivative at Zero
×
Maximizing Complex Number Product
✓
Maximizing Complex Number Product
□
Units Digit of Squares
✓
Units Digit of Squares
✓
Maximizing Z in Equations
✓
Maximizing Z in Equations
×
Sum and Integral Calculation
✓
Sum and Integral Calculation
×
Conjecturing Integral Properties
✓
Conjecturing Integral Properties
×
Complex Integral Calculation Timeout
✓
Complex Integral Calculation Timeout
□
Calculating Red Balls Quantity
✓
Calculating Red Balls Quantity
×
Finding Consecutive Even Numbers
✓
Finding Consecutive Even Numbers
×
Solving Floor Function Equation
✓
Solving Floor Function Equation
✓
Base Conversion of 1987
✓
Base Conversion of 1987
✓
Probability in Number Selection
✓
Probability in Number Selection
✓
Finding Specific Polynomial Function
✓
Finding Specific Polynomial Function
✓
Dice Probability Optimization
✓
Dice Probability Optimization
□
Continued Fraction Function
✓
Continued Fraction Function
✓
Zeta Function Sum Integration
✓
Zeta Function Sum Integration
□
Area of Inequality Set
✓
Area of Inequality Set
×
Proving Quadratic Roots Inequality
✓
Proving Quadratic Roots Inequality
□
Finding Circle’s Locus Equation
✓
Finding Circle’s Locus Equation
□
Solving Nested Radical Expression
✓
Solving Nested Radical Expression
✓
Finding Quadratic Integral Function
✓
Finding Quadratic Integral Function
✓
Sequence Analysis for 1001
✓
Sequence Analysis for 1001
✓
Calculating Function Value
✓
Calculating Function Value
✓
Minimizing a Mathematical Expression
✓
Minimizing a Mathematical Expression
×
Maximizing Fractional Exponential Expression
✓
Maximizing Fractional Exponential Expression
✓
Sequences Summing to 100
✓
Sequences Summing to 100
✓
Trigonometric Right Triangle Solutions
✓
Trigonometric Right Triangle Solutions
□
Quadruple Sum Calculation
✓
Quadruple Sum Calculation
×
Finding Quadrilateral Coordinate Value
✓
Finding Quadrilateral Coordinate Value
×
Finding Parabola Coefficient b
✓
Finding Parabola Coefficient b
✓
Evaluating Complex Infinite Sum
✓
Evaluating Complex Infinite Sum
×
Maximizing Quadrilateral Area Calculation
✓
Maximizing Quadrilateral Area Calculation
×
Maximizing Complex Mathematical Function
✓
Maximizing Complex Mathematical Function
✓
Integral Evaluation Steps
✓
Integral Evaluation Steps
✓
Simplifying Complex Rational Expression
✓
Simplifying Complex Rational Expression
✓
Proving Geometric Inequality
✓
Proving Geometric Inequality
✓
Calculating Positive Function Area
✓
Calculating Positive Function Area
✓
Finding Sequence Limit
✓
Finding Sequence Limit
✓
Matrix Power Limit Calculation
✓
Matrix Power Limit Calculation
×
Harmonic Progression Equation Verification
✓
Harmonic Progression Equation Verification
✓
Infinite Series Integral Calculation
✓
Infinite Series Integral Calculation
□
Identifying Non-Consecutive Sum Integers
✓
Identifying Non-Consecutive Sum Integers
✓
Checking Mathematical Conditions
✓
Checking Mathematical Conditions
□
Solving Helios’ Cattle Problem
✓
Solving Helios’ Cattle Problem
□
Finding Circle’s Maximum Radius
✓
Finding Circle’s Maximum Radius
×
Optimal Riemann Summation Method
✓
Optimal Riemann Summation Method
×
Complex Function Integration Calculation
✓
Complex Function Integration Calculation
□
Integral Convergence Condition
✓
Integral Convergence Condition
✓
Random Integer Distribution
✓
Random Integer Distribution
×
Prime Number Characteristics
✓
Prime Number Characteristics
✓
Prime Sum Combinations Count
✓
Prime Sum Combinations Count
×
Logical Problem Solving
✓
Logical Problem Solving
✓
Area of n-Powers Region
✓
Area of n-Powers Region
□
Solving Differential Equation
✓
Solving Differential Equation
✓
Coefficients in Cyclotomic Polynomials
✓
Coefficients in Cyclotomic Polynomials
✓
Minimizing a Mathematical Expression
✓
Minimizing a Mathematical Expression
×
Inequality Solution Intervals
✓
Inequality Solution Intervals
✓
Simplifying Trigonometric Expression
✓
Simplifying Trigonometric Expression
✓
Minimum of Trigonometric Function
✓
Minimum of Trigonometric Function
□
Maximizing e in Equations
✓
Maximizing e in Equations
×
"Good" Integer Problem Solution
✓
"Good" Integer Problem Solution
□
Solving Cryptarithmetic Puzzle
✓
Solving Cryptarithmetic Puzzle
×
Solving Trigonometric Equation
✓
Solving Trigonometric Equation
×
Finding Integer Triples
✓
Finding Integer Triples
✓
Calculating Inscribed Circle Radius
✓
Calculating Inscribed Circle Radius
✓
Expectation of Squared Distance
✓
Expectation of Squared Distance
✓
Finding Initial Calculator Input
✓
Finding Initial Calculator Input
✓
Choosing Integers Divisible by 3
✓
Choosing Integers Divisible by 3
□
Solving Polynomial for Integers
✓
Solving Polynomial for Integers
□
Finding Reversed Number
✓
Finding Reversed Number
✓
Finding Polynomial Roots
✓
Finding Polynomial Roots
□
Odd Integer Partition Counts
✓
Odd Integer Partition Counts
×
Puppy Weights Calculation
✓
Puppy Weights Calculation
✓
Calculating Real Number Distances
✓
Calculating Real Number Distances
×
Cosine Product Simplification Calculation
✓
Cosine Product Simplification Calculation
✓
Finding Tangent Curve Values
✓
Finding Tangent Curve Values
□
Finding Series Coefficient Formula
✓
Finding Series Coefficient Formula
□
Simplifying Trigonometric Expression
✓
Simplifying Trigonometric Expression
✓
Comparing Remainder Sums
✓
Comparing Remainder Sums
✓
Minimum of product
✓
Minimum of product
×
Finding Common Polynomial Roots
✓
Finding Common Polynomial Roots
✓
Minimizing Multivariable Polynomial Function
✓
Minimizing Multivariable Polynomial Function
✓
Maximizing Product with Constraints
✓
Maximizing Product with Constraints
□
Summing Fibonacci Series Expression
✓
Summing Fibonacci Series Expression
×

CITE THIS NOTEBOOK

100 Math problems: ChatGPT with Wolfram plugin vs the Code Interpreter Model​
by Michael Trott​
Wolfram Community, STAFF PICKS, June 5 2023
​https://community.wolfram.com/groups/-/m/t/2931334