let me see how can good you all are at use pf pencils :-P

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How many maximum squares can be constructed with use of 31 pencils of equal length on a table

The answer is 20.

1 solution

Suradnyana Wisnawa
Jun 4, 2014

Try to make a maximum number of square but using pencils efficienly, by using a pencil more than once if possible. Using 31 pencils of equal length can make a rectangle 3 x 4 of square 1 x 1. The total square are : 3x4 (1x1 square) + 2x3 (2x2 square) + 1x2 (3x3 square) = 12 + 6 + 2 = 20.

This question needs a lot more clarify. Please edit the question accordingly

1) It is not clear that you consider squares of different sizes.

2) I can arrange 15 vertical and 15 horizontal pencils which overlap, and give me a $15 \times 15$ grid of $1^2 + 2^2 + \ldots + 15^2$ squares.

Calvin Lin Staff - 7 years ago

I see. Thank you very much..
I'm sorry, when you arrange 15 x 15 grid, don't you need 32 pencils?

Suradnyana Wisnawa - 7 years ago

My grid referred to the grid lines, instead of the number of squares, hence the slight disagreement.

Calvin Lin Staff - 7 years ago

let me see how can good you all are at use pf pencils :-P

The answer is 20.

1 solution

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