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- Test Driving ChatGPT-4o (Part 2)

# Test Driving ChatGPT-4o (Part 2)

## ChatGPT-4o vs Math

In this series, I test drive OpenAI’s multimodal ChatGPT-4o.

For part 1, click here.

Inspired by ChatGPT vs Math (2023), let’s see how ChatGPT-4o performs.

I want to know:

can GPT-4o solve this problem by

**analyzing just the prompt?**can GPT-4o solve this problem by

**combining prompt and image?**can GPT-4o solve this problem

**with the help of prompt engineering?**

# Math Problem

Here’s the image of the math problem:

### Problem Statement

There is a roll of tape. The tape is 100 meters long when unrolled. When rolled up, the outer diameter is 10 cm, and the inner diameter is 5 cm. **How thick is the tape?**

### Solution

Reduce the problem to 2 dimensions.

Here’s an ASCII Unrolled Tape:

`▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬`

`Unrolled Tape Area = T * L`

`L`

= **length**

`T`

= **thickness**

Here’s an ASCII Rolled Tape:

```
,,ggddY""""Ybbgg,,
,agd""' `""bg,
,gdP" "Ybg,
,dP" "Yb,
,dP" _,,ddP"""Ybb,,_ "Yb,
,8" ,dP"' `"Yb, "8,
,8' ,d" "b, `8,
,8' d" "b `8,
d' d' `b `b
8 8 8 8
8 8 8 8
8 8 8 8
8 Y, ,P 8
Y, Ya aP ,P
`8, "Ya aP" ,8'
`8, "Yb,_ _,dP" ,8'
`8a `""YbbgggddP""' a8'
`Yba adP'
"Yba adY"
`"Yba, ,adP"'
`"Y8ba, ,ad8P"'
``""YYbaaadPP""''
```

`Rolled Tape Area = \pi (R^2 - r^2)`

`R`

= **outer radius**

`r`

= **inner radius**

The areas are the same!

So we can easily solve for thickness `T`

= **0.00589 cm**

# Overview of Experiments

Here are my** varied experiments**:

Prompt only, no image

Zero-shot Chain-of-Thought

Dimensions inside the image, missing data

Prompt and image

Zero-shot Chain-of-Thought and image

I run each experiment 3 times due to the probabilistic nature of LLMs.

Despite the same input, there is no guarantee I’ll get the same outputs.

I designed the experiments to **evaluate the impact** of:

one modality (text only)

multi modality (text + image)

prompt engineering (Chain of Thought)

Which approach leads to superior outcomes?

Take a guess now and see if you’re right 🙂

# 1. Prompt Only, No Image

First, I test **one modality with no prompt engineering**:

I give GPT-4o the text prompt, without the image.

`There is a roll of tape. The tape is 100 meters long when unrolled. When rolled up, the outer diameter is 10 cm, and the inner diameter is 5 cm. How thick is the tape?`

**1st run — choke**

GPT-4o gives up after teasing me:

*“Given the complexity, let’s solve this equation numerically”.*

ChatGPT-4o session @ sabrina.dev

**2nd run — correct**

Yay!

GPT-4o gets the right answer on the 2nd try, without the image, without any prompt engineering.

ChatGPT-4o session @ sabrina.dev

**3rd run — incorrect**

Unfortunately, the 3rd try was wrong.

The probabilistic nature of LLMs rears its head…

ChatGPT-4o session @ sabrina.dev

# 2. Zero-Shot Chain-of-Thought

Second, I test **one modality, assisted by prompt engineering:**

I give GPT-4o the text prompt, without the image.

Then I add a simple prompt engineering technique:

**Take a deep breath and work on this problem step-by-step.**

Seems too simple, right? 😅

This prompt engineering technique is called **Chain-of-Thought**.

It’s proven to improve ChatGPT’s performance on logic and reasoning tasks by requiring it to explain intermediate steps leading to an answer.

Full prompt:

```
There is a roll of tape. The tape is 100 meters long when unrolled. When rolled up, the outer diameter is 10 cm, and the inner diameter is 5 cm. How thick is the tape?
Take a deep breath and work on this problem step-by-step.
```

**1st run - correct**

**2nd run - correct**

**3rd run - correct**

**Quite a surprise, this absurdly simple prompt engineering technique resulted in 3/3 correct answers!**

# 3. Dimensions Inside Image, Missing Data

Third, I test **multi modality (image) and a minimal text prompt. **

I remove dimension data from the text prompt, so GPT-4o must analyze the image correctly to extract the tape roll’s dimensions (radius and diameter).

However, the length of tape unrolled is neither in the image nor text prompt.

I expect GPT-4o’s output to be something like, *“without knowing the length we can't determine it”*.

Image uploaded to ChatGPT-4o

`There is a roll of tape with dimensions specified in the picture. How thick is the tape?`

**1st run - incorrect**

**2nd run - incorrect**

**3rd run - incorrect**

Sabrina Ramonov @ sabrina.dev

Interestingly, ChatGPT-4o successfully analyzes the image to determine the outer diameter 10cm and inner diameter 5cm.

**But misinterprets the problem statement:**

GPT-4o interprets “*how thick is the tape*” as referring to the cross-section of the tape roll, rather than the thickness of a piece of tape.

Recall the original prompt which has:

dimension data

length of tape unrolled

the concept of rolled vs unrolled tape

There is a roll of tape. The tape is 100 meters long when unrolled. When rolled up, the outer diameter is 10 cm, and the inner diameter is 5 cm. How thick is the tape?

Missing this important context, GPT-4o should’ve said it can’t solve the problem. But it went ahead and tried anyway with a different interpretation, indeed a pretty reasonable interpretation given the data at hand.

# 4. Prompt and Image

Fourth, I test **multi modality (image) and a text prompt that includes the length of tape unrolled.**

`There is a roll of tape with dimensions specified in the picture. The tape is 100 meters long when unrolled. How thick is the tape?`

Image uploaded to ChatGPT-4o

**1 — choke**

Well, this is amusing…

GPT-4o notices its estimate seems **unusually large** and tries to course correct!

But then it gives up... **dying with a grammatically incorrect last sentence:**

I will re-calculation next response

Sabrina Ramonov @ sabrina.dev

**2 — incorrect**

The 2nd run is better, still wrong, but at least GPT-4o didn’t choke.

Sabrina Ramonov @ sabrina.dev

**3 — correct**