PrePrimary lessons aren't easy!

Discrete Mathematics Level 5

When Megh was small, his preprimary teacher was teaching counting of shapes.

She was teaching about this type of shapes and counting the number of triangles in them.For, example, the following shape has eight triangles

Imagine an \(n\times n\) grid made up of such boxes and count the number of triangles inside it. For example following is a \(4\times 4 \) grid

But when the teacher saw Megh scribbling in his notebook, she asked him to tell her the number of triangles in an \(4000\times 4000\) grid. To her surprise he answered the number of triangles \(x\) instantly.

Answer the digit sum of \(x\).

Details & Assumptions

  • This is but obviously a fake story inspired to be the one like Gauss's
  • The answer has been computer verified
  • Such a huge number was chosen to avoid use of computers
  • You might have to use a calculator to compute the answer
  • This problem was taken from Suganitam Magazine (where the answer is wrong. So, don't look :) )
  • If you are unclear, a \(2\times 2\) grid has 44 triangles.

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