# The Sherlock Holmes Problem Solving Challenge - Week 1

**Date:** 23rd Sep 2018 @ 2:42pm

*‘Sometimes the obvious answer to a case is the correct answer, Watson, while at other times there is more to it than first meets the eye. For instance, how many squares do you see in the grid below?’*

*'Write your answer below. Don't forget to explain your reasoning!'*

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Abigail R wrote:

Hi everyone!

What I did was I counted how many squares were on the top and side (just one side) rows and there was 9 squares on each one. This makes it so much easier to work out how many squares are in the grid. Plus, this is a much more efficient way to do the question instead of counting all the tiny squares. This was my final calculation...

9 x 9 = 81

There is a total of 81 squares in the grid.

Abigail :)

Hayden S wrote:

Unlucky

Jack T wrote:

very very unlucky

Mr Allen wrote:

Hi Abigail, well done for answering this question and justifying your answer. Unfortunately, that is not the correct answer.

Why don't you have another try...

Abigail R wrote:

Thanks for checking my answer Mr Allen! I will love to have another go at the question. Wish me luck!

Abigail :)

Abigail R wrote:

Hi everyone!

I'm back for another try at the question.Originally, I thought that it was just all the squares inside the grid. However, you have to include the actual grid as one square. Here is my final calculation...

9 x 9 = 81

81 + 1 =82

There is a total of 82 squares.

Abigail :)

Joseph L wrote:

I got the same answer as you doing the same things:)

John-Joseph S wrote:

Hello everyone what I did was count the rows then times the answer I got me to 90 I was looking at it for another answer but I couldn't find another one :P so 90 is my answer:)

Joe H wrote:

I found out that along with the other mini squares you could make other squares using the mini squares for example 4 mini squares together could make another bigger square.

so in total I got 138 squares

1 big square, 81 small, 16 made up of 4, another 16 made up of 4, and another made up of 4, 4 made up of 16 small squares, 1=5 by 5, 1=6 by 6, 1= 7 by 7, 1= 8 by 8.

not sure if I've over thought this

Joe H :)

Jack T wrote:

I have cracked the code! I realised there are squares made up from more than one square.

There are:

81 Squares made up of 1 square

16 Squares made up of 4 squares

9 squares made up of 9 squares

4 squares made up of 16 squares

1 square made up of 25 Squares

1 squares made up of 36 squares

1 square made up of 49 squares

1 square made up of 64 squares

THE ANSWER IS 115!

There is also a sequence in the number of squares. If you minus the number of squares from the next highest number of squares they always increase by 2

e.g.

4-1= 3, 9-4= 5, 16-9= 7, 25-16= 9, 36-25= 11, 49-36= 13, 64-49= 15

Hayden S wrote:

97 because 9 x 4 is around the edge but as you go further into the square it goes to 7 x 4 then 5 x 4 then 3 x 4 and finally there is one box left

Joseph L wrote:

Hi everyone! I'm pretty sure someone has one but I want a try. I did the same things as Abigail R . SUM :

9 X 9 = 81

But there is an extra one

81+1 =82

:)

Mr Allen wrote:

I love all of this Maths discussion (you know how much I love talking about Maths!!)

Mr Allen wrote:

Good afternoon Year 6.

Unfortunately, no one has the correct answer yet but some people are definitely on the right track! Like Sherlock says, ‘there is more to it than meets the eye!’

Keep trying!

Grace H wrote:

I have tried answering this question but there are LOADS, and I keep losing count !!!! It is harder than you think. If we counted all of the squares we would be 200 by the time we have finished counting !!!

Mr Allen wrote:

I wonder if you can think of a mathematical reason behind the answer then, Grace.

I'm glad it's got everyone thinking!

Who will be the first to solve it?

Olivia-Martine C wrote:

I counted all the squares and got 81????😶

Olivia-Martine C wrote:

Hello everyone!!

I got 82 because there is a big square around it and the squares individually is 81 add the one around it is 82 ! I think 💭

Faye H wrote:

If we count square s that don’t overlap there are 115: 81 (1x1);16(2x2);9(3x3);4(4x4); and 1(5x5);1(6x6);1(7x7);1(8x8);1(9x9) However if you count overlapping squares there are a lot more.There are 285 if you count overlapping squares

Euan B wrote:

Just trying to think out of the 'box', and it got me thinking about square numbers and there is 9 on the row across which means 9(no times button)9 which =81.

And 9 squared = 81 which means you need just 1 SQUARE number to fill the SQUARE

So the answer is 1!!!!!

Emily W wrote:

I realised that there are lots of different sized squares.

There are 1 x 1 squares, 2 x 2 squares, 3 x 3 squares, and so on until 9 x 9 squares.

9 x 9 squares = 1

1 x 1 squares = 81

But when you start getting on to the 2 x 2 squares they start to overlap so there are more than first meets the eye.

2 x 2 squares = 64

3 x 3 squares = 23

I started to count the 4 x 4 squares but it got quite complex because there were too many squares to count.

So I estimate that there are around about 350 squares.

by Emily Ward

Mr Allen wrote:

You're all working hard on this, Year 6! I'm very impressed!

Faye H wrote:

Is anyone write yet?

Emily W wrote:

Hey guys! Im back and having another go at the challenge. Ive worked it out and this is my answer. So, here I go:

1x1=1

2x2=4

3x3=9

4x4=16

5x5=25

6x6=36

7x7=49

8x8=64

9x9=81

Then you add the answers up, this is my workings out:

1+4=5

5+9=14

14+16=30

30+25=55

55+36=91

91+49=140

140+64=204

204+81=285

The total is 285

Mr Allen wrote:

Well done everyone! An excellent effort!

A couple of you have the correct answer...well done Faye and Emily.

There are 285 squares in total, as follows;

One square that is 9x9, four squares that are 8x8, nine that are 7x7, 16 that are 6x6, 25 that are 5x5, 36 that are 4x4, 49 that are 3x3, 64 that are 2x2, 81 that are 1x1.

I'll be putting next week's challenge on tomorrow!

Mr Allen wrote:

This week's challenge is now up everyone! Who will be the first to solve it?

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