A number of cats got together and decided to kill between them 999919 rats. Every cat killed an equal number of rats. Each cat killed more rats than there were cats. How many rats do you think that each cat killed ?

From the given equations,

(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
(6)2=14 + 2(ab + bc + ca)
36 - 14 = 2(ab + bc + ca)
22/2 = ab + bc + ca
ab + bc + ca = 11

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
= (6) (14 - 11)
=(6)(3)
=18

Since, a3 + b3 + c3 - 3abc = 18

36 - 3abc = 18

-3abc = 18 - 36

-3abc = -18

abc = 6.

Here the answer is 98.

The logic in the given puzzle:

2+3 = 8
3+7 = (7+2)x3 = 27
4+5 = (5+3)x4 = 32
5+8 = (8+4)x5 = 60
6+7 = (7+5)x6 = 72

Similarly,

7+8 = (8+6)x7 = 98.

The answer here is 1.

Logic Followed in the given puzzle ::

The logic here is the number of circles in each 4 digit number mentioned.

8801 has 5

5261 has 1

and so on

The Answer is 46.

Logic ::

First number on the right hand side is the second number in the left side of equation ( and ) second number on the right side is the sum of two numbers on the left side of the equation.

Hence, 2 + 4 = 4(2+4) = 46.

A + B = 15 .... (1)

B x C = 84 .... (2)

C ÷ 4 = 3  .... (3)

B + D = 18 .... (4)

From (3), we get C = 12

From (2), we get B = 84/12 = 7

From (1), we get A = 15 - 7 = 8

From (4), we get D = 18 - 7 = 11

Hence, D = 11.

The logic in this puzzle is summing the result of [subtraction of upper two digits] & [addition of lower two digits] 

Hence, the result is  

(5 - 3) + (2 + 8) = 2 + 10 = 12.

A - A - A = 20
B - B - B = 15
C - C - C = 25

A = -20
B = -15
C = -25

=> A + B + C = (-20)+(-15)+(-25) = -20 - 15 - 25 = -60.

5 + 5 = 10

5x 2 + 2 = 12

5 x 2 - 1 x 5 = 5

Hence, ∆ = 1.