Red Perimeter 3 – Working Backwards

Probability Level 1

If an $n \times n$ grid composed of unit squares has a red perimeter, and exactly 44 of the unit squares have exactly one red side, how long are the sides of the $n \times n$ square?

The answer is 13.

15 solutions

Chandrachur Banerjee
May 15, 2014

With the limitations of my thinking skills i happen to find a flaw in the question. It says : NUMBER OF SQUARES WITH - AT LEAST 1 RED SIDE - IS 44.Now that seems to include squares with red sides >=1 i.e with 2 red sides also. So the ans should be 4(n-1)=44 or, n=12. Plz inform if i went wrong.

according to me... it can be solved by a simple logic dear , actually.. the total number of small squares having one side red is 44. and all the sides would have same number of these type of squares.. soo one side will have 44/4=11 small squares with one red side...Now the first and the last square of each side has two red sides.. therefore thy are not included in this count,i.e, 11... and soo we can say.. that total no. of squares in one side = 11+2=13 .... as it is stated that each side has a unit length... soo, length of the n*n square = 13 units. :D

Rishabh Tripathi - 7 years ago

But adding this way counts the corner squares twice.

Shaquill Freeman - 6 years ago

Dude.. when we're talking of squares having one side red then we are not counting the corner squares. We are adding the corner squares at last just to get the length of the side.

Rishabh Tripathi - 6 years ago

didn't get the question~lol~

Tai Coong - 7 years ago

Sorry I didn't know what you want to do?

Parmar Padm - 7 years ago

44/4=11 and then give 4 edge blocks we get 13 blocks per side

Karan Bhosale - 7 years ago

With the answer n x n, where n=13 then if someone is given 13x13 and asked to create a pictoral version, they would not create the correct pictoral of n x n. This scenario is meant to fool for a false answer. In my opinion the proper question should have been to solve for the perimeter given that it is a level one question.

Cameron J. Grierson - 6 years, 9 months ago

ya i got the answer 12 how it is 13. i couldn't understand. please give the way

kalyani jha - 6 years, 7 months ago

Same here .

Akash Shah - 7 years ago

I agree. @Arron Kau , please change the wording of this question.

Sharky Kesa - 7 years ago

You are correct. I've fixed it to say "exactly one side" as that was the intent of the question. It got messed up during a previous edit. My apologies.

Arron Kau Staff - 7 years ago

No harm done.

Sharky Kesa - 7 years ago

I agree man the question is not correct

Rahul Maithani - 7 years ago

sorry i didnt get the question.. @Arron Kau

pallavi mohini - 7 years ago

But doesn't the question say "exactly one side"? Maybe it has been updated since this solution was posted.

Swati Singh - 3 years, 6 months ago

How long are the sides of square=how long is the perimeter of the square, I though that

Salah Amer - 7 years ago

Number of Squares with exactly 1 red side is 44. Read the question carefully.

Dhruv Tyagi - 6 years ago

Mikhaella Layos
May 16, 2014

Just equate 44 to the formula in the previous question, which is $4(n-2)$ . This gives us $4(n-2)=44$ $n-2=11$ $n=\boxed{13}$

Good and simple logic,thanks! K.K.GARG,India

Krishna Garg - 7 years ago

i can not understand this formula 4(n-2)=44... plzzzz tell me about this @ [email protected]

Muaz Mughal - 4 years, 7 months ago

Mohamed Sajjadh
May 16, 2014

44 SIDES HAVE ONE RED SIDE.IT IS A SQUARE SO FOUE SQUARE MUST HAVE TWO RED SIDE AT THE EDGE.ON SKETCHING THE DIAGRAM WE CAN FIND THAT ONE SIDE OF THE SQUARE MEASURE ABOUT 13 UNITS.. SIMPLE .... CONGRATZ FOR THOSE WHO TRIED IT ....

Nikhil Pallam Reddy
Jun 14, 2014

No. of squares with exactly one red side = 44. The corner squares will have two red sides. No. of small squares with exactly one red side on any given side of the bigger square = 44/4= 11. Adding the two corner squares, 11 + 2 =13. Hence, length of the square is 13 units.

Piyush Sarwariya
May 17, 2014

total no of square on the perimeter excluding the corner are 44 that's 11 on all sides adding the 2 corner pieces we get 13

Ahmed Hussain
May 17, 2014

the question is correct..remove one unit square from each corner f the big square because they have two sides red.hence u get 14 unit squares at each side..14 *4=56 single red colour squares..but we want total 44 single red colour unit squares,so divide 44/4=11..now.11 is single red unit squre..to get full length add 2,11+2=13..so,13 is ur answer

Sudarshan Kulkarni
May 17, 2014

No.... C... U have to do the calculations individually....

44÷4=11. 11 is the no. Of squares with only one side red...

Then add 2(non red sides)

Hence... 13

Philippe Arnoux
May 15, 2014

The correct formula is : (n - 2) x 4, we saw it in the previous item. So, let´s apply the formula on reverse : 44/4 + 2 = 13 The square is 13 x 13

Interesting but the ans is 13.

Chandrachur Banerjee - 7 years ago

2nd problem is to find the no of unit squares painted red on only one side for that we identified the formula as 4 (n-2) but in this question it says atleast one red side then answer should be 12 right ?

Jagadeshwar K - 7 years ago

Plz explain.

Bitan Nath - 7 years ago

@chandrachur - 2nd problem is to find the no of unit squares painted red on only one side so for that we identified the formula as 4 (n-2) but in this question it says atleast one red side then answer should be 12 right ?

Jagadeshwar K - 7 years ago

He did 44/4, but forgot the +2

Zaid Baig - 7 years ago

Thank you Zaid

Philippe Arnoux - 7 years ago

on May 11 Jagadeshwar K wrote 'it says at least one red side then answer should be 12 right ?' ...... ....... No - it would be 11, because it was still 44 small squares with at least one red side, which would include the corner small squares; and each corner small square belongs to 2 sides of the large square, so 44/4 = 11

Jerry Hollands - 6 years, 7 months ago

Swati Singh
Nov 29, 2017

Each corner unit square has 2 sides which are included in the red outline. Each side of the big square has 2 corner squares. Since the 44 unit squares mentioned in the question have only 1 red side, they do not include the corner unit squares. Each side has n-2 (excluding the two corner unit squares) unit squares which are part of the 44 unit squares, therefore (n-2)x4 = 44. Solving this, n-2= 44/4, then n-2 = 11, n = 11+2 and finally n=13.

got it @Swati Singh Paraste

Prajwal OP - 1 month, 2 weeks ago

Akhil Guru
Aug 6, 2014

The only pieces with 1 red side are the non-corner edge pieces. We have 44 of those and are given the fact that our figure is a square. This means there is an equal number of 1-red-sided pieces on each side of the figure, and 44/4 =11. There are 11 non-corner edge pieces per edge, and each edge has two corners, giving us 13 total pieces per edge.

Kawaii Kuma
May 25, 2014

Just remember the square in the corner of the bigger square has 2 side colored red

Prajwal Kavad
May 24, 2014

From the previous problem we get: 4(n-2)=44

n-2=11

hence n=13

Stupendous Sairam
May 21, 2014

Its simple there r 4sides and 4cubes should not be taken at 4 vertices and as there r 4sides each side have 44/4 cubes and 2cubes should be taken in to account which r at corners of side of square. So 11 plus 2 gives 13

Mona Mazen
May 18, 2014

From the previous problem: 4(n-2)=44 n-2=11 n=13

Shohag Hossen
May 15, 2014

4( n -2) = 44 , so, n=13.

Red Perimeter 3 – Working Backwards

The answer is 13.

15 solutions

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