Number Puzzles Questions

Adding the corresponding numbers in first and last figures gives the corresponding number in the middle figure.

i.e, 4 + 3 = 7

13 + 2 = 15

2 + 4 = 6

9 + 1 = 10

We can make an equation:

3(100000 + x) = 10x+1

(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)

Solving this gives:

10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x = 299999/7 = 42857

The answer is 42857 (142857 is three times smaller than 428571).

The missing number in the given number puzzle is "78".

Here the logic is the numbers are from 86 - 91 when we read upside down.

The logic in the given puzzle is 

4 + 4 = 4 * 4+1 = 4 * 5 = 20

5 + 5 = 5 * 5+1 = 5 * 6 = 30

6 + 6 = 6 * 6+1 = 6 * 7 = 42

7 + 7 = 7 * 7+1 = 7 * 8 = 56

Similarly

9 + 9 = 9 * 9+1 = 9 * 10 = 90.