## ChatGPT and Mathematics (III)

GPT-4 was just released. Here’s a preview of what it’s capable of. I tried throwing some mathematics problems at it to check out its capability.

## Problem 1: Cheryl’s Birthday Problem

There’s an infamous logic problem from Singapore’s primary school Olympiad training. Here’s the full problem from the Wikipedia page (quoted verbatim).

And… here’s the output.

That’s correct: the first line of deduction tells us the month is July or August.

Correct!

Ok, but this is a well-known viral problem. Maybe let’s try something a little different.

## Problem 2: Combinatorics

Here’s the problem.

I’d say it’s a decent inter-school level type of problem. Here’s the output:

A little of a bummer, since it incorrectly thought there must be four +1 and four -1 in each row. But the penultimate paragraph is impressive. So maybe a little nudging would help?

Result:

Extremely impressive!

## Problem 3: Construction Problem

Here’s a rather tricky problem. [ Hint: the smallest solution is close to a million. ]

The astute reader immediately sees the problem with this “solution”: 1118 has sum of digits = 11, which is a multiple of 11. I pointed it out; GPT-4 then responded with another 4-digit (wrong) example. I pointed out again and it responded with another wrong example. At this point, I gave up.

To avoid cluttering up the reader’s bandwidth, I won’t be sharing those wrong answers.

## Problem 4: PSLE Coin Problem

This problem from PSLE 2021 again caused some controversy due to its perceived difficult:

Here’s part of the answer I got:

Right at the start it made the wrong assumption: that Helen and Ivan have the same number of 50-cent coins. I pointed this out:

Then GPT-4 realised its mistake:

But it still wouldn’t tell me who has more money. Guess wealth is a sensitive question even for a few dozen bucks.

I nudged it further:

And:

Goal!!

## Problem 5: Group Theory

Here’s one which can be quite tricky if you’re unfamiliar with concrete examples of groups.

Long story short: it tried to come up with three examples, failed, and concluded that such an example is impossible. What impressed me was the diversity of its examples. It tried to use:

1. $\mathbb Z \times \mathbb Z_2$.
2. The free group $F(a,b)$.
3. The dihedral group $D_4$ of order 8.

The astute reader should immediately know why each of these examples fails.

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