The Password Riddle

My father challenged me today on JD 10 to solve this riddle. I’m sure it slipped out of his mind that I’m majoring in Accounting. But hey, a little extra cash won’t hurt anybody

By the way, I found it so easy that it took me couple of seconds to figure it out. And yes I got the money!

Here goes:

A man wanted to get into his office building, but he had forgotten his password. However, he did remember five clues:

- The fifth number plus the third number equals fourteen.
- The fourth number is one more than the second number.
- The first number is one less than twice the second number.
- The second number plus the third number equals ten.
- The sum of all five numbers is 30.

What are the five numbers?

So go ahead and use your brain to solve something for a change

But if you are fed up by now—and cursing me—hit the Read More button to see the solution.

Okay, so let’s start simple.

Let’s say that the 5 numbers are A B C D E

1) We take the clues one by one:

- The fifth number plus the third number equals fourteen →  E + C = 14

- The fourth number is one more than the second number → D = B + 1

- The first number is one less than twice the second number → A = 2B - 1

- The second number plus the third number equals ten → B + C = 10

- The sum of all five numbers is 30 → A + B + C + D + E = 30

2) We arrange the 4th equation to C = 10 - B and then solve for the 1st equation to become E + 10 - B = 14

3) We solve for all the equations in term of B:

     - E + 10 - B = 14 → E = 4 + B

     - D = B +1

     - A = 2B - 1

     - C = 10 - B

4) We then substitute the previous equations in A + B + C + D + E = 30

A + B + C + D + E = 30

(2B - 1) + (B) + (10 - B) + (B + 1) + (4 + B) = 30
2B - 1 + B + 10 - B + B + 1 + 4 + B = 30 
2B - 1 + B + 10 - B + B + 1 + 4 + B = 30
4B + 14 = 30
B = 4

5) We then simply figure out the rest of the terms:

     - A = 2B - 1 → A = 7

     - C = 10 - B → B = 6

     - D = B + 1 → D = 5

     - E = 4 + B → E = 8

6) Here we go, the password is: 74658

Hope you like it just as I did… Okay okay just don’t hit me