Divide by 12 to get a remainder.

Take any prime number like 19.
Square it and add 14.You will get 361+14=375
Now divide by 12,you get 3 as reminder.
Even if you take any other prime number and work similarly,you will get the same remainder.
If you add 17 instead of 14,you will always get 6 as the remainder.
Even if you take any odd number not divisible by 3 instead of any prime number,you will have similar results..

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Repeat a number

Take any three digit number like 134.
Repeat the same number by its side making a 6 digit number 134134.
Divide this now by 7,You get 19162.
Divide now by 11,You get 1742.
Divide now by 13.You will get the original 3 digit number 134.
This procedure holds good for any 3 digit number chosen.

Envelope trick

I wish to present a trick which you can play with your friends/relatives.
It is better to have at least 4 persons before you for this as otherwise the trick is likely to be discovered,though not always.You will write a number say 43 on a piece of paper without showing it to anybody,place it in an envelope and close it shut.
You will then present a sheet of paper containing 16 numbers in 4 rows/4 columns.You will give one person a coloured pencil say green asking him to score out one row and one column..Another person with a red pencil to score out another row/column.A third person with blue pencil to score out another row/column.The last 4th person to score out the last row/column with say an yellow pencil..
The green colours meet at a particular number in the grid.Similarly the other colours will meet each at a different number in the grid.You will then ask the persons to add up all the 4 numbers where each set of coloured pencils meet .They will be surprised to find that the total is 43,which you have written and placed in the closed envelope.
The 16 numbers which you have written in the sheet of paper presented for scoring out will be as follows-
14,16,11,10
 9, 11, 6,  5
 8, 10, 5,  4
17,19,14,13.
How do you find the trick?
I have given below two more grids below for numbers 51 and  103-
Number 51-Numbers given row-wise--(8,11,17,13)..(12,15,11,17)...(14,17,13,19)..(10,13,9,15)
Number 103--(26,24,35,32)....(24,22,33,30)...(19,17,28,25)...(21,19,30,27)   

Magic squares-4/4 cells

I have so far dealt with 3/3 cells.
Let me now deal with 4/4 cells formed with numbers 1 to 16-
I will first show how the magic square can be formed by way of steps-
Step 1-You write down the 16 numbers in 4 rows/4 columns,starting with 16 first,and going down upto 1.
Step 2-The numbers in the 2nd and 3rd columns are now changed to read from bottom to top-viz the 2nd column will now read as 3,7,11,15 instead of 15,11,7,3.same step in 3rd column.
Step3-The numbers in the 2nd and 3rd columns are now interchanged.
Step 4-The numbers in the 2nd and 3rd rows are now altered by reading from right to left,viz for example the 2nd row will now read as 9,7,6,12 instead of 12,6,7,9 .same process 3rd row.
Step 5-The numbers in the 2nd and 3rd rows are now interchanged.
You will now find the magic square  as follows-shown in groups of each row-
(16,2,3,13)...(5,11,10,8)...(9,7,6,12)..(4,14,15,1)....The totals of each row,column and both diagonals will be 34..This is a total which is double the sum of the first and last number viz twice (1+16).
Same procedure can be followed for forming squares with any consecutive 16 numbers.
Also by taking the first 16 even numbers  or 16 odd numbers,or starting with  any even or odd number.