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In the reaction of tri-iodination of 2-methyl propane only five isomers can be formed, from which only the branch methyl can be iodinated if both the lateral carbond are iodinated .. Is this because of the inductive effect or the steric effect is the responsible here...if it is the steric effect which hinder the iodination of the branch carbon (2-methyl) why is it possible to tri-iodinate the lateral carbons( the primary carbons other than the branch one) ?

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The reason only five isomers can be formed is the three methyl groups are equivalent by symmetry.

Isomers

I believe your arbitrary distinction of branch carbon/methyl from lateral carbon/methyl is creating confusion

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