Question

A flying saucer crashes in a Nebraska cornfield. The FBI investigates the wreckage and finds an engineering manual containing an equation in the Martian number system: 325 + 42 = 411. If this equation is correct, how many fingers would you expect Martians to have?

Answer 1

Answer:

6 fingers

Step-by-step explanation:

Let X = the base of the numbers above

If X > 0

Then we have:

325 = 3 * X² + 2 * X¹ + 5 * X°

325 = 3X² + 2X + 5

42 = 4*X¹ + 2*X°

42 = 4X+ 2

And

411 = 4*X²+ 1*X¹ 1*X°

42 = 4X² + X + 1

Since 325 + 42= 11 then

3X² + 2X + 5 + 4X+ 2 = 4X² + X + 1 ------ Collect Like Terms

3X² - 4X² + 2X + 4X - X + 5 + 2 - 1 = 0

-X² + 5X + 6 = 0 ------- Multiply both sides by -1

X² - 5X - 6 = 0 ------- Factorise the Equation

X² - 6X + X - 6 = 0

X(X - 6) + 1( X - 6) = 0

(X + 1)(X - 6) = 0

X + 1 = 0 or X - 6 = 0

X = -1 or X = 6

But X>0

So, X =-1 is invalid

X = 6

The expected number of fingers of the Martian is 6