Quadrilaterals again!

Probability Level 4

If the figure in the left is figure 0, the one in the middle is figure 1 and the one in the right is figure 2, then find the number of quadrilaterals in figure 2016 which follows this pattern.

The answer can be expressed as $n^2$ , find the value of $n$ .

The answer is 2017.

2 solutions

Abhay Tiwari
Apr 17, 2016

Ashish, this q. Was fun. Keep posting :)

Try this one .

https://brilliant.org/problems/recursive-division-its-beautiful/

Thank you very much Abhay, I shall surely solve your question later, going zzz now. But plz tell me wheter the divisions are applicable for only one part of the square. In your question(figure) the divisions are shown only diagnally. Great problem otherwise, way to go.

Ashish Menon - 5 years, 1 month ago

Ashish it is for one side only, sorry for replying late, even I went to sleep after commenting. :p

Abhay Tiwari - 5 years, 1 month ago

Great, it was a great question, but forgot to include the biggest square :V but with a different approach.

Ashish Menon - 5 years, 1 month ago

Ashish Menon
Apr 17, 2016

The number of quadrilaterals in figure 0 = 1.
The number of quadrilaterals in figure 1= 4.
The number of quadrilaterals in figure 2 = 9.

We observe that the number of quadrilaterals in the nth figure is {(n+1)}^2
$\therefore$ In 2016th figure, there would be ${2017}^2$ quadrilaterals.

$\therefore n = \boxed{2017}$

Can you prove by induction? Great problem.

Mateo Matijasevick - 5 years, 1 month ago

Thank you very much, I shall try and post afterwards got to go zzz now :P

Ashish Menon - 5 years, 1 month ago

exactly same way I did!!! :-) :-)

Atul Shivam - 5 years, 1 month ago

☺☺Great ;)

Ashish Menon - 5 years, 1 month ago

Quadrilaterals again!

The answer is 2017.

2 solutions

0 pending reports