In each diagram, the central value equals the sum of the left and right hand numbers, minus the sum of the upper and lower numbers. So, (9 + 13) - (4 + x) = 16 22 - 4 -x = 16 x = 18 - 16 x = 2.

As you move left to right the diagram, double each number and subtract 5 to give the next number. So, Missing number = 21 * 2 - 5 = 37.

As you move left to right work down the column, numbers follow the sequence of Square Numbers from 16 to 81, subtracting 4, then 8, then 12 etc. So, 4 * 4 - 4 = 12. 5 * 5 - 8 = 17. 6 * 6 - 12 = 24. 7 * 7 - 16 = 33. 8 * 8 - 20 = 44. Missing number = 9 * 9 - 24 = 57.

Logic (Row-wise): Central Number = Difference of the sum of the odd numbers and sum of the even numbers in the row. So, X = 7 - 2 = 5. Missing Element = 5.

Splitting the diagram into 3 smaller triangles, with 3 circles each, the sum of the numbers in each smaller triangle is always 21. So, 3 +7 + 11 = 21. 5 + 12 + 4 = 21. 10 + 10 + x = 21. x = 1. Missing Number = 1.

Working left to right, double each number and subtract 5 to give the next number. So, Missing number = 37 * 2 - 5 = 69.

Starting with the top left segment, and moving clockwise around the circle, numbers follow the sequence of square numbers, from 121 to 256. 11* 11 = 121. 12 * 12 = 144. 13 * 13 = 169. 14 * 14 = 196. 15 * 15 = 225. 16 * 16 = 256. Missing Element = 196.

Add together numbers in corresponding segments of the outer four squares. The answer is placed in the diagonally opposite segment of the middle square.

Working in columns, the sum of the numbers in each column equals 18.

Starting on the top left, and moving clockwise in a spiral towards the centre, numbers increase by 7, then decrease by 2. Repeat this pattern all the way around. So, Missing Number = 18 - 2 = 16.

Reading each line of the diagram as a 3 digit number, add the top and middle lines together to give the result on the bottom line. Thus, 237 + 645 = 882. Missing Element = 2.

Logic (Row-wise): Left Element + Right Element - 2 = Central Element. 7 + 3 - 2 = 8. 3 + 2 - 2 = 3. 6 + x - 2 = 5 x = 1.

Working through the diagram in columns, the value at the bottom of each column equals the sum of the top 2 numbers, minus the sum of the next 2 numbers. So, (3 + 21) - (4 + 9) = x 24 - 13 = x x = 11.

In each grid, working in columns, add the top and bottom numbers together, and put this sum in the centre square in the grid underneath the original (for the top grids), or the grid above (for the lower grids). So, 5 + x = 13 x = 8.

In each star, the value at the centre equals the difference between the sum of the top 3 numbers and the sum of the bottom 3 numbers. (5 +6 + 4) - (2 + 1 + 3) = 9. (11 + 4 + 8) - (7 + 3 + 2) = 11. (9 + 9 + 2) - (6 + 4 + 5) = x x = 20 - 15 x = 5.

Logic: (Sum of outer four element )/2 = Central Element. So, Required Number, = ( 1 + 8 + 6 + 3)/2 = 9.

Logic: First number + second number - 4 = Third Number. 3 +6 - 4 = 5 6 + 5 - 4 = 7 5 + 7 - 4 = 8 8 + 7 - 4 = 11 11 + 8 - 4 = 15 15 + 11 - 4 = 22. So, Missing number = 22.

First Circle: Multiplication of to upper numbers /2 = Lower number. = (8 * 4)/2 = 16. Second Circle: Multiplication of to upper numbers /3 = Lower number. = (8 * 9)/3 = 24. Third Circle: Multiplication of to upper numbers /4 = Lower number. = (12 * 9)/4 = 27. Missing Number = 27.

Step 1 Take values in the top left and centre circles and put their sum in correspond- ing segments of the lower left circle. Step 2 Take values in the middle and right hand circles, and put their difference into corresponding segments of the lower right circle. Missing Number = Lower Right Segment of Middle Circle - Lower Right Segment of the Right Segment. Missing Number = 7 - 2 = 5.

Reading each row as a whole number, multiply the top 2 digit number by the lower 2 digit number to give the result represented by the middle 3 digit number. Thus, 12 * 21 = 25x 25x = 252. So, x = 2.

Logic: Add up numbers in corresponding segments of each square. The sum of the digits in the left hand segments = 20, The sum of the upper segments = 22, The right hand segments = 24 The lower segments = 26. Thus, 13 + 2 + 7 + x = 26. x = 26 - 22 = 4. Missing Element = 4.

The Sequence 2, 4 , 3, 7 , 5, 11, 8, 16, 12, x can be divided into two sub sequence such as 2, 3, 5, 8, 12 and 4, 7, 11, 16 , x. For First Sequence, 2 2 + 1 = 3 3 + 2 = 5 5 + 3 = 8 8 + 4 = 12. For Second Sequence, 4 4 +3 = 7 7 + 4 = 11 11 + 5 = 16 16 + 6 = 22. So, Missing Element = 6.

Starting with the top circles, multiply each value by 2 and subtract 3, writing the result in the corresponding segment of the lower circle. So, 8 *2 = 16 - 3 = 13. Missing Number = 13.

Numbers in boxes from the second row up equal the average of the 2 numbers in the boxes directly below. Continue to the apex of the triangle. Thus, Missing Number = Average of 7 and 5. Missing number = (7 + 5)/2 = 6.

As you move left to right, numbers follow the sequence of Square Numbers, from 36 to 121, subtracting 10 for the second number, 20 for the next, then 30 etc. So, 36 49 - 10 = 39 64 - 20 = 44 81 - 30 = 51 100 - 40 = 60 So, 121 - 50 = Missing Number Missing Number = 71.

Logic (Column-wise): Upper element - Middle Element = Lower element. So, Missing Number = 7 - 6 = 1

Logic: (Previous Number + 1 ) * 3 = Next Number. So, Missing Number = (282 + 1) * 3 = 849.

Taking the top 3 numbers, add them together, and write the 2 digit result in the spaces below. Repeat this pattern for the next set of numbers. So, 9 + 9 + 2 = 20 Thus, 3 + 3 + 5 = Missing Number Missing Number = 11. Missing Digit = 1

Logic (Column-wise): Top Element + Middle Element + 1 = Bottom Element. So, 3 + 5 + 1 = 9. 2 + 2 + 1 = 5. 6 + 1 + 1 = 8. Missing Element = 8.

Logic: Sum of the Four Number at the corner of the square = 21 and Sum of the Four Number at the middle of the square = 21. Now, 7 + 5 + 6 + 3 = 21 5 + 7 + x + 8 = 21 x = 1. Thus, Missing Number = 1.