Solution:

10968

Water image is 89601

Solution:

Marshall lives in House no.36
Robin lives in House no.4
Barney lives in House no.9
Lily lives in House no.35
Lyndsy lives in House no.24

Solution:

42857

Let the number be x
10x +1 = 3(100,000 + x)
=> x = 42857.

Solution:

4100

some people might guess 5000

Solution:

Total Number of Matches: 63
Explanation:
32+16+8+4+2+1 = 63

Solution:

9+8+7+65+4+3+2+1+0

Solution:

The only number is 2592. 2^5 is 32 and 9^2 is 81. 32*81 is 2592.

Solution:

47 + 53 + 59 + 61 = 220

Solution:

100/9 (fraction number is also a number)

lets say 'X' is the number.
10/X = X - 10
9X = 100
X = 100/9

Solution:

The required number is 236 and the sum is 11.

It is given that the first two digits of the required number are prime numbers i.e. 2, 3, 5 or 7. Note that 1 is neither prime nor composite. Also, the third digit is the multiplication of the first two digits. Thus, first two digits must be either 2 or 3 i.e.
22, 23, 32 or 33 which means that there are four possible numbers - 224, 236,326 and 339.
Now, it is also given that - the difference between it's reverse and itself is 396.
Only 236 satisfies this condition. Hence, the sum of the three digits is 11.