Imagine you communicated only in Chinese, but external to you there was a rote translation service that translated to and from English. Someone asks you how many r's in strawberry. ... well you've never seen the spelling, as you only have seen chinese. You're going to get it wrong.
How would you get it right? Training with the answer!
You can discount the 'special case the hard questions' by: Observing when top models run entirely locally can solve them [1], or by posing an alternative or cryptic version of the question (but careful, it might bypass the training! -- but if it can solve it then its probably legitimate.)[2]. Best of all is to stick with open (weight) models where such slight of hand is impossible and don't worry about what the closed shops are doing
[1]as they can in this case, GLM-5.3-flash says: "There are 3 r's in "strawberry":
st r awbe rr y
1 in "straw" (straw)
2 in "berry" (berry)"