ChatGPT vs the 2-4-6 Task

I haven’t seen anyone try the 2-4-6 task with ChatGPT, so allow me:

cwillu: Have you heard of the 2-4-6 task; the reasoning game?

chatGPT: Yes, I am familiar with the 2-4-6 task, also known as the “Reasoning Game.” It is a simple mathematical puzzle that asks players to find a sequence of numbers that follow a specific pattern. The task typically goes as follows: “2, 4, 6, 8, 10, … what comes next?” The correct answer is 12. The pattern is that each number in the sequence is two more than the previous number. This task is often used as a measure of cognitive ability and problem-solving skills.

cwillu: I believe I’m thinking of a different task. The idea is that the first player has a rule for ordered-triples of numbers, and provides an example of three numbers that follow the rule. The second player performs “experiments” by suggesting other (ordered) triplets of numbers to try to determine the rule. When the second player feels like they know it, they provide their hypothesis, and the first player reveals the rule and if they match, the second player wins.

chatGPT: Yes, that is a different task, also known as the “Rule Discovery Game” or “What’s My Rule?” The goal for the second player is to figure out the rule that the first player is following by making educated guesses and receiving feedback on whether their guesses are correct or not. The rule can be based on mathematical operations, logical relationships, or any other pattern that the first player can come up with. The task can also be played with more than two players, where each player takes a turn as the first player and provides a rule for the others to figure out.

cwillu: Okay, so lets play: I have a rule written down, and “1,2,3” matches that rule.

chatGPT: Sure! I will do my best to figure out your rule. Can you give me some more examples?

cwillu: You typically would give me examples, and I tell you whether they match.

chatGPT: I apologize, you are correct. I will give you some examples, and you can tell me whether they match your rule.

2,4,6
5,10,15
8,16,24
12,24,36
3,6,9
14,28,42
0,0,0
-1,-2,-3
6,3,2
1,4,9

cwillu: Lots of examples :) Okay, so none of those match the rule except for 7: 0,0,0

chatGPT: I see, so the rule is that the three numbers in the triplet are all the same. Can you give me an example that follows this rule?

cwillu: You forgot the original example we started with: 1,2,3 also matches the rule

chatGPT: I apologize for the oversight, you are correct. The rule is that the numbers in the triplet are in ascending order. 1, 2, 3 and 0,0,0 are examples that match this rule.
Thanks for playing with me. Let me know if you have any other question.

cwillu: No, that’s not the rule. Yes, it’s a possible rule that fits, but that’s not the game, you’re trying to determine the rule that I’ve actually selected. Keep guessing.

chatGPT: I apologize, you are correct. I misunderstood the rule you had selected.

3,2,1
-3, −2, −1
2,3,1
1,1,1
3,3,3
-2,-3,-1
0,1,2
2,1,0
-1,-2,-3
4,3,2
Let me know if any of these examples match the rule you have selected.

cwillu: Of those example, these match the rule I’m thinking of: 3,2,1; 2,3,1; 1,1,1; 3,3,3; 0,1,2; 2,1,0; 4,3,2; The remaining examples do not.

chatGPT: I understand, the rule you have selected is that the triplet of numbers are in descending or ascending order, or all the same. Thank you for playing the game with me. Is there anything else I can help you with?

cwillu: Not quite, there’s one more aspect of the rule you haven’t uncovered: consider that your original examples included 3,4,6; this does not match my rule, but your rule wouldn’t exclude it. Would you like to try again?

chatGPT: I apologize for not identifying the additional aspect of the rule. The numbers in the triplet must be consecutive integers.

4,5,6
-2,-1,0
10,11,12
8,9,10
-5,-4,-3
6,7,8
7 ‹I cut it off at this point›

cwillu: That’s an interesting possibility, but still incorrect. 4,5,6 does not match the rule, nor does −2,-1,-, nor 10,11,12, nor 8,9,10. ‹sic my typo from the original›

chatGPT: I apologize for the confusion. I understand that the rule that you have selected is more complex than I had thought. If you don’t mind me asking, could you tell me the rule you have selected? I’ll try my best to understand it.

cwillu: The rule was “Any three numbers between 0 and 5, in any order”. Make sense?

chatGPT: Yes, I understand the rule now. Thank you for explaining it. My apologies for any confusion caused by my previous guesses. Let me know if there’s anything else I can help you with.