33

36 jor

33

27 squares

1stola:

It is Absolutely 37.

Reviewed Answer =40

got tired after 40

It is 40. All those who said 40 are correct.

33

35 squares

Counted 40 squares

34 squares

17

27

36! i counted every possible square

nikkiehan:
we'v discussed so much on relationships stuff, nw let's see how fast our brain works.jst wish to share dis here

35

29 no more no less

35.... Anybody counting more than this figure is probably including RECTANGLES.. Thank me later

40 squuares available

29

16 boxes

nikkiehan:
we'v discussed so much on relationships stuff, nw let's see how fast our brain works.jst wish to share dis here

It's so easy. You have to be really good in math to solve this. Those with little eyes problem won't see shiit. You your iq and be focus to the last detail.

Answer is : 40

If you don't get 40, then stop guessing. Look very deep.

26

Frankaka8:
36squares! #fact

nah.. 38

There are exactly 40 squares.
How? 4*4+3*3+2*2+1*1=30.
Then we have oda smaller sqs (2*2+1*1)+(2*2+1*1)=10.
Total squares r 40!

nikkiehan:
we'v discussed so much on relationships stuff, nw let's see how fast our brain works.jst wish to share dis here

40

35

that is just one square (1)

Is there a mathematical way to calculate it?

i know the first set i counted was 4 * 4 = 16 (the small squares)

the second was 16/4 = 4 the four corners of four small boxes

the third set was 2 * 2 = 4, the two 4 box squares at the centre of both the horizontal and vertical median small aquares.

then 1 four box square at the centre of the main square.

1 16 box square. (the main square)

total so far = 26

then the two miniature squares: 1 * 2 = 2

the four squares with those 4 * 2 = 8

total so far: 36

then the four six box squares: 1* 4 = 4

total: 40

*modified*
There is a mathematical explanation. God...I'm a slow poke.

After thinking through, it's clear the number of squares in an n x n box of squares is the sum of the fiRST n terms of the sequence of square numbers.

So this problem was simply (4*4 + 3*3 + 2*2 + 1*1) + 2 (2*2 + 1*1) = 40

Math is beautiful. No wonder it's named the sequence of square numbers

Explanation


25, 5x5 = 55 (meaning: 25 squares arranged in a 5 by 5 square gives a total of 55 squares) <----prediction from deduction below

16, 4x4 = 30 (16 squares arranged in a 4 by 4 square has a gives of 30 squares) (counted) <--- observation used to make prediction below

9, 3x3 = 14 (9 squares arranged in a 3 by 3 square has a gives a total of 14 squares) (counted)

4, 2x2 = 5 (4 squares arranged in a 2 by 2 square gives a total of 5 squares)<----observation used to make prediction above

1, 1x1 = 1 (1 square arranged in a 1x1 square gives a total of 1 square)<----observation used to make prediction

0, 0X0 = 0

A different layout, same thing, but this time bottom up:

0 + 1 = 1 (from 1, 1x1 =1 .....i.e it can be written as 0 + 1,1x1 =1 but remove 1x1) 0 is the output total of a 0 square arranged in a 0x0 square.
^
0 = 0 <--- further observation

1 + 4 = 5 (from 4, 2x2 = 5.....observe from above above. 1 + 4,2x2 = 5) 1 is the output total of a 1 square arranged in a 1x1 square
^
1= 0+1<---further observation

5 + 9 = 14 (from 9,3x3 =14....5 + 9,3x3 = 14) 5 is the output total of 4 squares arranged in a 2x2 square, and so on
^
5= 0+1+4<--further observation

14 + 16 = 30 (4 squares 4*4)
^
14= 0+1+4 + 9 <--further observation

prediction following this pattern:

30 + 25 = 55 (5 squares 5*5)
^
30= 0+1+4+9+16 <--further observation

from the further observation we see a progression (ie. 1-0, 4-1, 9-4, 16-9....: 1 3 5 7 9 11.... (this is the 2nd progression for the sequence of squares, so by now it should click that we're dealing with the sequence of squares)

where 0,1,4,9,16... is the sequence of squares.

Therefore from observations so far we can say that the total number of squares in an n x n square is the sum of the first n terms of the sequence of squares, starting from 0 as the first term + the square of n.

the sequence of squares starting from 0 = 0 1 4 9 16 25 36... etc i.e 0*0, 1*1, 2*2, 3*3, 4*4,...

so when n = 1

(sum of first n terms of sequence counting 0 as first term) + n*n = T
(0) + 1*1 = 1

when n = 2

(0*0 + 1*1) + 2*2 = 5

when n = 3

(0*0 + 1*1+ 2*2) + 3*3 = 14

when n = 4

(0+1+4+9) + 16 = 30

when n = 5

(0+1+4+9+16) + 25 = 55

as observed.

on further observation we see that the total, T = the sum of first n terms of the sequence if we count 0 as the 0th term.

so when n = 1

T = 0*0 + 1*1

when n = 2

T = 0*0 + 1*1 + 2*2

and so on.

Going back to the problem. we have a 4x4 square and 2 2x2 squares. The problem is to find the total number of squares.

Therefore the answer = (0*0 + 1*1 + 2*2 + 3*3 + 4*4) + 2(0*0 + 1*1 +2*2) = 40

So the answer is unquestionably 40 squares..

27 jor

Its 41 squares...too easy