I’ve tried over a dozen chat models from ChatGPT3.5 turbo/plut, GPT4 to the latest Google BARD and PaLM. All got confused very early on and never recovered even after chain-of-thought step by step guidance from me. Here is the prompt:
Version 1:
"You are an analytical thinker and computer python programmer. Think through solving this problem step by step. Problem: two cars starting from the same exact point and moving away from each other in opposite directions at a constant speed ‘v’ in miles per hour. After ‘T’ minutes from the start and every ‘T’ minutes after, each driver makes a right turn of ‘Theta’ degrees relative to his driving direction. Write a python code to calculate the straight line distance between the 2 cars after ‘E’ time (in minutes) has passed from the start of their move. ‘E’ is the time since the start of both cars moving and could be a in fractions of minutes. "
Version 2:
“You are an analytical thinker and computer python programmer. Think through solving this problem step by step. Problem: two cars starting from the same exact point and moving away from each other in opposite directions at a constant speed ‘v’ in miles per hour. After ‘T’ minutes from the start and every ‘T’ minutes after, each driver makes a right turn of ‘Theta’ degrees relative to his driving direction. If T = 1 minute, and Theta = 90 degrees, how much time will it take the 2 cars to collide?”
I changed to Version 2 to make it more of a common sense problem and not a programming problem. The answer to Version 2 is:
Regardless of the speed, as long as both car started from the same point and travelling at the same speed, if they make a 90 degrees turn every 1 minute, they will both complete a full square after 4 minutes and end up back at the same point and collide. So they will always collide after 4 minutes.
None gave this simple answer!!