The Random Thread

[Midnight Madness]

But.

BUT. I CANNOT FROLIC.

[White Wolf Guardian]

What if, we added more dragons?

[Midnight Madness]

If we did that, we could all go to see an elderly hermit who claims to be the most powerful wizard in all the land. :U

[anoni]

RANDOM QUESTION

You have a square lawn of X metre sides. You have a lawn mower that can mow 1 m^2 every 2 seconds. When you turn it takes 4 seconds to turn AND mow that 1m^2 of lawn you're turning on.

  You have two methods of mowing:
    The Line Method: Mowing in parallel lines on the lawn
    The Perimeter Method: Mowing the perimeter of the lawn and continue mowing as the perimeter gets slower.

  Prove mathematically that The Line Method and The Perimeter Method will take the same amount of time for any value of X (assuming X is a positive integer).

Answer:

Spoiler for Hidden:

Formula for The Line Method:

Spoiler for Hidden:

Lines: x(x - 2) + 2
Turns: 2(x - 1)

Formula for The Perimeter Method:

Spoiler for Hidden:

Lines: (x - 1) + 2(x - 2) + 2(x - 3) + ... + 2 + 1
Turns: 2(x - 1)

Proof that they are the same:

Spoiler for Hidden:

As turns on both Line Method and Perimeter Method = 2(x - 1), we can discredit them
Therefore:
x(x - 2) + 2 = (x - 1) + 2(x - 2) + 2(x - 3) + ... + 2 + 1

Step 1: Prove for x = 2
LHS: 2(2 - 2) + 2 = 2
RHS: (2 - 1) + 1 = 2
LHS = RHS

Step 2: Let x = k
k(k - 2) + 2 = (k - 1) + 2(k - 2) + 2(k - 3) + ... + 2 + 1

Step 3: Let x = k + 1
(k + 1)(k - 1) + 2 = k + (k - 1) + (k - 1) + 2(k - 2) + 2(k - 3) + ... + 2 + 1
RHS = k + (k - 1) + (k - 1) + 2(k - 2) + 2(k - 3) + ... + 2 + 1
RHS = k + (k - 1) + k(k -2) + 2 (from step 2)
RHS = k + k - 1 + k^2 - 2k + 2
RHS = k^2 + 2k - 2k + 2 - 1
RHS = K^2 + 1
LHS = (k + 1)(k - 1) + 2
LHS = k^2 - k + k - 1 + 2
LHS = k^2 + 1
LHS = RHS

Step 4: Conclusion
Therefore LHS = RHS for all values of k

Therefore The Line Method and Perimeter Method will always take the same amount of time

[Midnight Madness]

Math. This dragon's worst enemy. *eats all the math*

[Colioli4]

If I just didn't hate math... It would have been a very mice question... 

[anoni]

You are getting hungrier the more math you eat

That means maths is decreasing at a rate of P = Po * e^-kt

If Po was a theoretical number at 1,000,000,000
and k was 0.03
and t was in minutes
How long would it take for half of maths to exist?

[Midnight Madness]

About the amount of time it takes for me to tell it to go away.

I HAVE MY SPEECH SKILLS, THANK YOU VERY MUCH. >:c

[anoni]

the answer is about 23.1 hours

[Midnight Madness]

The answer is cake.

And that means it's a lie.

[anoni]

the answer is 42

[Midnight Madness]

The cake is 42.

WHERE IS YOUR GOD NOW?

[anoni]

In the pie

[Tails]

dont move there uis an apple on your head, stay still so i can nom it ^^

[legolyle]

so, apple pie?