I wouldn't say she's the most intelligent, Sakura was always book smart in part 1, while Sasuke copied answers, Naruto answered none, Sakura was the only one to fill out the Chunin exam test answers. It was ultimately Naruto's plan that beat Kakashi
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, used his clone to analysis Kakuza's fighting style and make a plane
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, Setting a trap that fool Kakuza and lead to his defeat
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, Creates a dust cloud using rasengans while a clone transforms into FRS while another clone jumped into the air to almost kill 2 of Pains last bodies until Deva path powers returned
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, was the only person to figure out how the 3rd Raikage to get his scar when the whole cloud village couldn't figure out, saving him and Sasuke from Obito by connecting them to Minato via chakra arm, figuring out Juubito's weakness, plan with Kurama and Minato to connect chakra, add senjutsu to tbb.
Sasuke's fight with Deidara has many feats of smart moments, he analyzed Deidara's jutsus, test them out then used that knowledge to defend and attack. Smart even to kill Oro when he was bedridden instead of becoming his next body, was smart to know to keep pushing Danzo so Izanagi gets used up, Smart enough to not fall for Sakura's little trick to gain his trust, smart to use Juugo's chakra with his Susanoo.
They all have battle smarts but I think Sakura is superior in general knowledge/book smart while Naruto and Sasuke are higher in battle smarts. I know they all have other feats but no point to go that in-dept, from what we seen I'll put Naruto's battle smarts first, then Sasuke then Sakura while in general knowledge I put Sakura first then Sasuke and Naruto last. Analyzing skills would go Sasuke, Naruto, Sakura with Sasuke winning due to the Sharingan and Naruto because I was impressed who effectively he used his clone to analyze Kakuza's skill and it's a shame that Kishi felt he needed to stop Naruto from doing that in his fights to keep him from being too strong. He alsomade use of Minato's jutsu after recently learning how it works. Sakura shown more analyzing feats earlier on in shippuden but Naruto has shown more from mid to current and that's why Sakura isn't above Naruto in the analyzing for me.