number pattern for:

white tiles is
3,6,10,15

grey tiles is
1,3,6,10

all tiles is
4,9,16,25


(a)
first, do u see a pattern of squared factor?
square of 2 is 4;
square of 3 is 9;
square of 4 is 16;
square of 5 is 25; ...

In Fig. 1, total no. of tiles is 4
now, how to convert 1 to 2?
we can add 1 to 1 and get 2.

So for Fig. 1, square of (1+1) = 4

next, for Fig. 2, square of (2+1) = 9
.
.
.

So, for Fig. 5, square of (5+1) = 36

Ans: 36


(b)
Look at the number pattern for grey tiles versus white tiles.

Can u see that the number pattern for white tiles is "one step" in advanced of the number pattern for grey tiles?
OR the grey tiles number pattern is "one step" behind that of white tiles?

Now the number pattern for grey tiles is:
1,3,6,10

Looking at white tiles' number pattern, the next number for grey tiles shld b 15.

Now figuring out the link between Figure number and tile number:

In Fig. 1, no. of grey tiles is 1
In Fig. 2, no. of grey tiles is 3
In Fig. 3, no. of grey tiles is 6
In Fig. 4, no. of grey tiles is 10
In Fig. 5, no. of grey tiles shld b 15

Can u see the difference between 1 and 3? ans: 2
between 3 and 6? ans: 3
between 6 and 10? ans: 4
between 10 and 15? ans: 5

So for Fig. 6, no. of grey tiles is 15+6 = 21

and so on...



But for White tiles,
In Fig. 1, no. of white tiles is 3
In Fig. 2, no. of white tiles is 6
In Fig. 3, no. of white tiles is 10
In Fig. 4, no. of white tiles is 15
In Fig. 5, no. of white tiles is 21

(Fig. 2)= 3+(2+1) = 6
(Fig. 3)= 6+(3+1) = 10
(Fig. 4)= 10+(4+1) = 15
(Fig. 5)= 15+(5+1) = 21
(Fig. 6)= 21+(6+1) = 28

and so on....

let u figure out for Fig. 10


(c)
using above for grey tiles, u can work this out on ur own. :)




hope this helps.