Trickster's ball

[Demonic God]

The other day, I headed to the Golemus Laboratory, for some experimentation. Tinkering around, messing with the Aramors to-be-filled with AI cores.

Alas, such work is boring! So boring indeed, that half way through, as my attention span dictate... I decided to make a very, very bouncy ball. A drop of blood, glue, rare minerals... and Voila!

Throwing this thing in open space, would be unwise. Not that it would do any damages, but I prefer to not lose my shiny possessions. So, I had a small room built, and gave it a throw. Alas... I did not expect it to bounce so vigorously, the damn thing bounced so well, catching it would be impossible! As I ponder upon this dilemma, miraculously, the ball bounced straight back at me. Damn thing almost broke a tooth of mine, but I did managed to catch it. Impressed by this outcome, I laid down my pen and paper, and begins working out, how exactly did the ball bounce back to exactly where I was? And how many times, did that damn thing bounced around?

So, I ask for your help, to determine the numbers of bounces the ball made. Here are the details of how it all went down - according to my memory:

• The ball somehow ignored gravity, and flew parallel to the ground at all times
• I started at the South-West corner of the room
• The ball was thrown perfectly North-East. (45 degree)
• The room is almost a square, of dimension 2020 cm x 2021 cm. I fully intend to sue the contractor for this error.

Summarized in mathematical terms:

• You throw a perfectly bouncy ball in a rectangle (2020 x 2021) room from a corner
• The ball was thrown at a 45 degree angle
• The ball ignored gravity, and flew parallel to the ground at all time
• How many bounces did the ball make before it return to your location?

Rewards:

• Most elegant solution - 1 Anni crit
• Most creative/unorthodox solution - 1 Anni crit
• Fastest correct solution - 1 GC
• All correct solutions - 5SC + 1 spell stone
  • Lock in chaos
  • Acoustic Remains
  • Teleport to Papercabin

Edited April 15, 2021 by Demonic God
adjusted some wordings

[Tissy]

Hello mind crusher. 

[Demonic God]

Quest posted

[Demonic God]

I announce that Lady @Aia del Manahas submitted a correct solution, being the first to done so, 28 minutes after the quest was posted!

Amazing, and congratulations!

[Demonic God]

Closing submission in 12 hours, congrats to all solvers!

[Demonic God]

Here is the final list of all who submitted a correct solution!

• @Aia del Mana
• @Aelis
• @Dracoloth
• @Fyrd Argentus
• @Tissy
• @Trola
• @Yoshi

Please let me know which spellstone you want here or via PM. I'll try to get them to you before the next anni

Also:

Lady Aia wins an extra GC for having a correct solution less than30 minutes after the quest went online!

As for the anni crits - well, it's hard to say, rather, since there was two particular methods that people used to solve this problem:

1. Observing that the balls slowly move towards the two corners, 1 cm at a time, every 2 bounces. Thus, it took 2020 (smaller edges) x 2 (bounces per cm) x 2 (back and forth) - 1 = 8079 bounces
2. Tracing the bounces for smaller n/(n+1) rectangles, and finding a general formula of 4 * n - 1.

As such, the winners were selected as the solutions that stood out the most to me, for each of this category. Hence:

1. Tissy wins an anni, for a creative solution (that actually resembles a general case solution for any n x m rectangle and any starting launch angle, that I know of). While he did eventually returned to the 1cm logic, his way of reaching it stood out
2. Yoshi wins an anni, for observing the pattern (with pictures demonstrating the bounces) for smaller rooms, before concluding on the general formula.

[Aia del Mana]

Many thanks for this quest, Demo; I would like the lockinchaos spellstone, if it please thee.

[Demonic God]

Notable mention would be Steno, who did send in an outside-the-box submission jokingly stating that there's no way to tell, since the construction crew could've screwed up the walls and resulted in strange bounces!

I was tempted to give him the creativity award, but sadly, as we all know, his current lack of access to a computer (and busy hosting various quests too), prevented him from giving me a theory on how the wall deforms could've looked like

[Dracoloth]

I'd like the teleport to paper cabin spellstone

[Aelis]

Teleport to Paper cabin stone for me as well, please

 

[Tissy]

Thanks DG for the interesting puzzles. 

I'd like an acoustic remains stone. Thanks.

[Trola]

Teleport to Paper cabin stone please