Number Puzzles Questions

Sum of all numerals must be ten because each numeral stands for the count of other numerals and because this number shall have ten numerals. Beginning to choose reasonable numerals for the first figure you can come across the correct number: 6210001000.

Here in the given number puzzle, the given numbers follows a pattern that 

1 + 4 = 5 => 1 x 4 + 1 = 4 + 1 = 5 

2 + 5 = 12 => 2 x 5 + 2 = 10 + 2 = 12   

3 + 6 = 21 => 3 x 6 + 3 = 18 + 3 = 21 

Similarly, 

8 + 11 = 96 => 8 x 11 + 8 = 88 + 8 = 96  

Hence, the missing number in the given number puzzle is 96.

In the given number puzzle,

Sum of Row 1 = 14

Sum of Row 2 = 23

Sum of Row 3 = 13 + ?

Sum of Column 1 = 16 

Sum of Column 2 = 23 

Sum of Column 3 = 11 + ?

Diagonal 1 sum = 17

Diagonal 2 sum = 14 + ?

From the above analysis,

Sum of Row 2 = Sum of Column 2 = 23

Sum of Row 1 = Sum of Column 3 = 14 = 11 + ?    .............(1)

Sum of Row 3 = Sum of Column 1 = 16 = 13 + ?    .............(2)

Diagonal 1 sum = Diagonal 2 sum = 17 = 14 + ?    .............(3)

Hence,

From (1), (2) & (3)

? = 3

Working in columns, the sum of the numbers in each column is always 14

Starting with the 10 at the top, one set of numbers increases by 3 each time, written in alternate boxes as you move down the diagram, and the other set of numbers decreases by 2,written in the boxes remaining

Here in the given number puzzle, the logic is

column 2 x column 3 = column 1

3 x 3 = 9

2 x 3 = 6

Similarly,

4 x ? = 8

=> ? = 8/4 = 2.

Looking at the diagram in  rows, the central circle equals half the sum of the numbers in the other circles to the left and right of the centre.

Given

6 = 3 => Number of letters in SIX = 3

12 = 6 => Number of letters in TWELVE = 6

14 = 8 => Number of letters in FOURTEEN = 8

Similarly,

22 = 9 => Number of letters in TWENTY TWO = 9

Therefore, 22 = 9.