magic square sudoku 10

A partially filled 16x16 grid is given below

4					12					10					2
	11			3							1			9
		13					5	7					15
			6			14			16			8
			2			10			12			4
		9					1	3					11
	15			7							5			13
8					16					14					6
	3			11							9			1
12					4					2					10
			14			6			8			16
		5					13	15					7
		1					9	11					3
			10			2			4			12
16					8					6					14
	7			15							13			5

                                      

                                           GIANT SUDOKU 16x16

                                                 

Fill in the grid with numbers from 1 to 16 in such a way that every row, every column ,every 4x4 box, each corner to corner diagonal accommodates numbers 1 to 16 without repeating any.  Also, each 4x4 box is a magic square of order 4.

squares and rectanglges

One 5x5 geometrical pattern is given below.

 

 

How many squares are there in the illustration ?

How many  rectangles are there in the illustration?

Is there any formula to determine the number of squares and rectangles?

the star

Place the numbers from 1 to 19 in the circles of the star diagram given above so that the sum of 5 numbers in any line is equal to 46.