Red Perimeter 5 – Big Square

Probability Level 2

Given that an n × n n \times n square made of unit squares has been painted red on its perimeter, and that there are at least 1000 unit squares with no red sides, what is the smallest value n n could be?

This problem is part of Arron's set The Red Perimeter .


The answer is 34.

View wiki
Arron Kau by Arron Kau

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Arpit Sah
May 15, 2014

1024 is the first four-digit square, i.e. the first square after 1000.

Therefore, to get smallest value of n, we would consider that 1024 unit squares are with no red sides.

( n − 2 ) 2 ( n - 2 )^2 = 1024 1024

( n − 2 ) 2 ( n - 2 )^2 = 3 2 2 32^2

( n − 2 ) ( n - 2 ) = 32 32

n n = 34 34

12 Helpful 0 Interesting 0 Brilliant 0 Confused

exactly the same thinking... (Y)

Harshvardhan Mehta - 7 years ago

Good work.

K.K.GARG.India

Krishna Garg - 7 years ago

From prev : (n-2)^2>=1000. The nearest square next to 1000 is 32^2. So (n-2)^2=32 n=34.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Prajwal Kavad
May 24, 2014

(n-2)^2 >=1000.

The closest square next to 1000 is 32^2.

So (n-2)^2=32, hence n=34.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...