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MANIFOLD
Are there more than 100,000 squares in a piece of graph paper? (Subsidized M100)
11
Ṁ350Ṁ1.8k
resolved Sep 13
Resolved
NO

Is anyone able to calculate the rough value of the number of squares in a piece of graph paper, specifically five star 3 ring graph paper? I'm quite curious on the best way to solve this question. Will resolve to the most convincing comment.

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There are less than 2000 1x1 squares and less than 50 squares per 1x1 square so the answer is clearly NO.

predictedNO

@n1psey that is pretty darn clean

Each square has precisely one top left corner.

Each grid point is a top left corner for squares of size between 1 and the smaller of the distances from it to the right and bottom edge.

There are 32x43 unit squares in the picture.

Putting it all together:

There should exist a closed form solution but this works

@CodeandSolder Actually, the closed form is quite simple, there are 1x1 squares with a top left corner in each point except the ones on the bottom and right row, 2x2 from all except their last two and so on, so a sum for x[1-32] of x*(x+11)

Wolfram helpfully tells us:

Which after substituting 32 for x gives us 17248.

Which, after remembering how range() works checks out:

@CodeandSolder magic numbers boo

I think 1/4in squares are common so an 8.5in x 11in sheet would have 8.5*4*11*4 = 1496 squares. If it was A4 paper with some metric sized squares it would be the same order of magnitude.

predictedNO

I now understand that I misunderstood the question entirely <shame>