Numbers in the segments of the upper left hand circle equal the product of the numbers in corresponding segments of the lower 2 circles, and the numbers in the segments of the upper right hand circle equal the sum of the numbers in corresponding segments of the bottom two circles.

Working from the bottom row to the apex of the triangle, the sum of the values in each row follows the sequence 15, 14, 13,12. 8 + 2 + 1 + 4 = 15 7 + 3 + 4 = 14 6 +7 = 13 So, Top Element = 12.

First Row, Middle Digit = First Element + Last Element + 2 11 = 7 + 2 + 2 Second Row, 14 = 6 + 4 + 4 Third Row, 19 = 5 + x + 6 So, x = 8.

5 2 *5 - 4= 6 2 * 6 - 3 = 9 2* 9 - 2 = 16 2 * 16 - 1 = 31. Missing Number = 31.

Start anywhere on the diagram, and move clockwise, calculating the sum of every third circle. This always equals 15.

Row-wise: 7 +2 + 6 = 15 3 + 9 + 3 = 15 So, 5 + 4 + x = 15 x = 6.

Logic: Next number ( Even Placed ) = Previous Number + Sum of the digits of previous number. Next number ( Odd Placed ) = Previous Number + Sum of the digits of previous number - 12. 79 = 71 + 7 + 1 ( Even Placed ) 67 = 79 + 7 + 9 -12 ( Odd Placed ) 80 = 67 + 6 +7 ( Even Placed ) 68 = 80 + 8 + 0 - 12( Odd Placed ) x = 68 + 6 + 8 = 82( Even Placed ) Thus, Missing number = 82.

Logic (Row-wise): Right hand element = Sum of the odd numbers in the row 4 = 3 + 1 7 = 7 8 = 5 + 3 So, x = 0 Because there is no odd number in the last row.

Logic (Column-wise): Sum of the element in each column = 21. So, 6 + 12 + x = 2. x = 3.

Calculate the sums of the numbers in the left and right hand circles, to give 2 digit answers. Write the left hand answer in the top 2 segments of the central circle, and put the right hand answer in the bottom 2 segments of the central circle. So, 3 + 6 + 1 + 8 + 9 + 2 = 29. 4 + 4 + 3 + 2 + 7 + 1 = 21. So, Missing element = 21.

In each diagram, multiply the left hand number by the upper central number to give the central number one line down, and multiply the right hand number by the upper central number to give the lower central number. So, 7 * 3 = 21. 7 * 8 = 56.

As you go left to right, alternately subtract 8 to give the next number, then divide by 2. Now, 26 is divide by 2 to give 13. So, Missing number = 13 - 8 = 21.

Logic (Left to Right): 44 = 12 * 12 = 144 (Remove First Digit) = 144 69 = 13 * 13 = 169 (Remove First Digit) = 69 96 = 14 * 14 = 196 = 96 25 = 15 * 15 = 225 = 25 56 = 16 * 16 = 256 = 56 Similarly, Missing Number = 17 * 17 = 289 ( Remove first digit) = 89.

Add the number at each corner of the diagram to its 2 adjacent numbers. The total is always 15. 4 + 4 + 7 = 15 5 + 4 + 6 = 15 6 + 7 + 2 = 15 So, 6 + 2 + x = 15 x = 15 - 8 = 7.

In each diagram, add up the 4 outer numbers then add 2 for the left hand group, 4 for the next, then 6, then 8, and put this result in the central circle. So, Missing Number = 7 + 3 + 5 + 6 + 8 = 29.

In each diagram, multiply the numbers shown on the arms together and add the number at the very top to give a 2 digit result, written in the lower 2 spaces. So, 50 = 6 * 8 + x. x = 2.

In each square, multiply the top and bottom numbers together to give a 2 digit result, and write this result in the left and right hand spaces. So, 6 * 2 = 12. Missing Element = 2.

Multiply the 2 numbers in the outer segments together and add 1 to give the value in the inner segment opposite. So, Missing Number = 5 * 2 + 1 = 11.

Split each grid into 2 halves, vertically, leaving 2 columns, each 2 squares wide. Start with the top left pair and move down, then to the top right pair, and down again. Reading each pair of digits as 2 digit values, the 2 digit values increase by 11, 12, 13, 14 and 15.

The average of the numbers in each column is always 4. So, Missing Element = 4.

Using the top two grids as a source, numbers in the lower left grid equal the sums of numbers in corresponding positions of the top two grids, subtracting 1 each time, and numbers in the lower right grid equal the differences between numbers in corresponding positions of the top two grids, adding 1 each time.

Logic (Row-wise): Central Row = Sum of the other rows. So, 4 + 5 + 8 + x = 18 x = 1. Missing Number = 1.

Starting with the numbers in the top two circles, add numbers in the left hand segments of each circle, and put these values in the left hand segments of the lower left circle. Put the difference between segments in the right hand halves of the two top circles in the right hand half of the lower left circle. Repeat this pattern for the lower right circle, but putting the difference between numbers in the left hand half of the top two circles in the left hand half of the lower right circle, and the sum of the right hand half of the top two circles in the right hand half of the lower right circle. So, Missing Number = 6 + 2 = 8.

Starting From Bottom row, Add numbers in adjacent boxes and put the sum in the box directly above. So, Missing number = 16 + 17 = 33.

Reading each row as a 4 digit number, from top to bottom, rows follow the sequence of Cube Numbers from 16 to 19. So, In the last row, there will cube of 19 i.e. 19 * 19 * 19 = 6859. Missing Element = 9.

Take any group of 5 numbers along the side of the square, and their total is always 25. So, 5 + 6 + 1 + 4 + x = x + 3 + 3 + 2 + 8 = 25. x = 9.

In each star, the number in the centre equals the difference between the sum of the numbers in the upwards triangle and the sum of the numbers in the downward triangle. So, For First Star, (4 + 9 + 2 ) - (3 + 1 + 6) = 15. Second Star, (6 + 8 + 5) - (7 + 3 + 1) = 8. Third Star, ( 6 + 9 + 1) - (6 + 1 + 2) = X X = 7.

Divide bigger square in four smaller square. Then, Central Number of each smaller square = sum of the each number at Corner. So, 14 + 3 + x + 11 = 47. x = 19.

Split the diagram into 3 columns, each 2 spaces wide, and read each double space as a 2 digit number. Starting at the top of each column, add the 2 separate digits together, then add this to the whole 2 digit number, to give the result, written in the spaces underneath.

Working through the diagram in rows, find the difference between the left and right hand values, then add 2 to give the value in the central space. So, Missing Element = 5 - 2 + 2 = 5.