Number Puzzles

Answer: 4
Explanation: Diagonal numbers are multiplication of the bottom number and 3
8*3 = 24
5*3 = 15
x*3 = 12 =? x = 4

Answer: 15
Solution:
If you see there are 3 variables and 3 equations, we can solve the equations and get the variables values and than we can find the value of fourth equation.

From the first equation we can say that ColdDrink = 10
than from the second Burger = (20 – 10)/2 = 5
and from the third equation FrenchFries= (9 – 5)/4 = 1

Thus Burger + FrenchFries * ColdDrink = 5 + 1*10 = 15

here as per BODMAS 5 + 1*10 will be 5 + 10 = 15

-1^n is 1 (if n is even) OR -1 (in n is odd)

but in this equation power is on 1 not -1
-1¹²¹-1¹²² -1¹²³-1¹²^⁴ = -1-1-1-1 = -4

Answer: 665
explanation:
it follows this equation 3^n – 2^n where n is integer starting from 0

thus
3^0 – 2^0 = 1 – 1 = 0
3^1 – 2^1 = 3 – 2 = 1
3^2 – 2^2 = 9 – 4 = 5
3^3 – 2^3 = 27 – 8 = 19
3^4 – 2^4 = 65
3^5 – 2^5 = 211
3^6 – 2^6 = 729 – 64 = 665

There is one more way to solve this

3*previous number + 2^(n-1)

0x3+1=1;
1×3+2=5;
5×3+4=19;
19×3+8=65;
65×3+16=211;
211×3+32=665;

wondering how it is possible?

lets solve 3*previous number + 2^(n-1)

=> 3*(3^(n-1) – 2^(n-1)) + 2^(n-1)
=> 3^n – (2+1)*2^(n-1) + 2^(n-1)
=> 3^n – 2^n – 2^(n-1) + 2^(n-1)
=> 3^n – 2^n i.e. our first equation