Logic Puzzles with OpenAI o1

I really like this puzzle because it's been a puzzle from a computer game I've been playing as a kid the riddle reads as a princess is as old as the prince will be when the princess is twice as old as the prince was when the princess's age was half the sum of their present age even it even reads hard kind of like it takes a while for a human to understand and translate this problem into how to actually solve it the question is what is the age of the prince and a princess and let's ask our our reasoning model how it will do with that and again we can observe a little bit it's its thinking process for like decoding the problem uh understanding what are what are the equations that the ages of prince and princess need to fulfill and let's see for how long the model will need to think about it just similarly as humans sometimes think longer and shorter on a problem our models do the same thing and after the while I hope the model will give us a correct answer here the model is still thinking about it it's not the easiest problem but we got the answer just right now the model also like walks us through the solution in this case what are the variables what are the conditions how to translate this problem into English and how to solve those equations where they are just real time together we even got a message about verification and we got we got the answer where where the princess's age is 6 * k for any natural number K and princess's age is 8 * K that natural age which also like is the correct solution for the problem in that game