Open Heroes’ Experience
Introduction
Your role as a Mentor is to role-play the Episode with your Hero(es). Making the Episode fun and engaging is serious business, so get ready to put your role-playing hat on!
The approximate prep time for the Mentor is 10 minutes and the play time with the Hero(es) is 10-15 minutes for Heroes of ages 10+.
In this sample Episode, one of the rebels has fallen into a trap and she needs to find the lock code to escape. To help her, the Heroes must master manipulating even and odd numbers, along with division and multiplication, before answering the Episode Challenge.
The Episode contains some backstory and then a Challenge. At first glance, the note in the Challenge: “From the God of Prophecy’s Sacred Number you must start. With the length of its Hailstone Number Sequence you must end..” looks impossible to understand. You, as the Mentor, come to their rescue by providing hints on how to gather evidence to decipher the Challenge, as well as by using the Skill Acquisition Module (SAM) to teach them the concepts that will help them solve the Challenge.
Instructions
1. LAY THE GROUNDWORK FOR YOUR HERO(ES) JOURNEY episode
Please read all the material beforehand (Episode Story, SAM) and go through the Episode yourself so you know what the answer to the challenge is, and how to smoothly go over the SAM with your hero(es).
To set up the experience you need two things:
Either print these instructions, or have them handy on your mobile phone or computer in a way that the Heroes cannot access.
Set up a browser window (we recommend Google Chrome) on a desktop or laptop, where the Hero(es) can interact with the story. The window/tab should point to:
https://www.studiosparky.com/challenges/sewers-hero
2. time to role play!
Put your role-playing hat on and tell the Hero(es) you have something fun for them today!
3. tell the story
Expose the Hero(es) to the Episode Story on the Terminal.
The Terminal will ask for a codeword in order to activate. Tell them the codeword is ‘sewers’.
Then ask them to press ENTER to proceed. If part of the message is not visible due to the size of the window, simply scroll down/up using the mouse or trackpad on their device.
4. explain the god of prophecy
You may let them web search who is the God of Prophecy and what is their Sacred Number (answer: Apollo and 7).
Provide hints if they get stuck.
5. explain the hailstone numbers
Encourage your hero(es) to search the web for the “Hailstone numbers”. They should find a connection to the Collatz Conjecture, described in SAM.
As they attempt to get the answer, tell them that you know what the Hailstone Numbers are and that you can teach the Hero(es) so they can find the 4-digit code.
6. help them with the sam
Go through the SAM with the Hero(es).
7. Solve the Challenge. Here is how to do it:
A web search shows that the God of Prophecy is Apollo and Apollo’s Sacred Number is believed to be 7.
The Hailstone Number Sequences and how to compute them are explained online after a quick web search, but can also be found in Step 3 of the SAM.
The length of the sequence for 7 is 16, as explained in the SAM. This is a great place to make this lesson interactive. Ask your hero(es) to play a game with you, where you take turns computing the next number in the Hailstone Sequence of the number 7.
We also know from the Story that we have a 0, which if we read the note in the Challenge carefully, must be “the No Number”.
So we know the 4-digit code is made up of the digits 0,1,6,7 and we know it must end in 16, so there are two choices: either 7016 or 0716.
The Challenge says you must start with Apollo’s number (7) and end with the length of its Hailstone Number Sequence, 16.
Final answer is 7016.
8. celebrate!
episode reference
Story
Hey Partner...
I’m not sure how I got into this jam. Totally not my fault. I was just taking some initiative, is all. And now I’m locked up in a cell stripped of all my sweet tools and comms in one of WormWood’s million underground labs. Real nice place this is. With a view. Of the sewers. My Squad will never find me.
Look, all I wanted was to “borrow” one of his notebooks so my Squadies and I can figure out how to fight those scary WormCtapods he made, like the one patrolling right outside. Real friendly dude with sharp claws. Winning personality too. With its single-eyeball stare.
At least my Terminal to You still works inside my earring. Ha! WormWood’s scanners can’t see old tech like that. So I hope you’re readin’ this, Partner. Because...
Challenge
I gotta get outta here, pronto! If it helps, I saw this note written on a piece of paper stuck on a board nearby:
“From the God of Prophecy’s Sacred Number you must start. With the length of its Hailstone Number Sequence you must end. And between the two there is the No Number to set.”
WormWood sure is a cryptic history nut. My cell has a 4 digit lock and a number pad. Thanks to the wonderful moisture of the sewers on the number pad I see someone pressed 0 and 6 recently, but I don’t see the other two. I bet you I’m only gonna get a couple of chances before an alarm goes off. Since WormWood has not yet destroyed the Web in your timeline, can you make sense of his note and send me the 4-digit code so I can get the heck outta here??
Answer
7016
Correct Answer, Riddle Piece
Sweet! You got me out, Partner! To reach me in the Quantum Terminal again here is a riddle for you: “How many B’s in the word Bibblybeebopbbbbeep”
Wrong Answer
Oh no! It didn’t work. Please, please, pleeeeease, don’t let me rot in this cell.
SAM
the hailstones!
When a number is divisible by 2, which means it has zero remainder upon division by 2, we call it Even. Otherwise we call it Odd.
Step 1
Ask the Heroes to divide the number 16 by 2. Is it even or odd? How about 15 divided by 2?
Answer: 16/2 = 8. It divides perfectly by 2 so it’s Even. 15/2 = 7 with remainder 1, so it’s Odd.
Step 2
Ask the Heroes to multiply 7 by 3 and then add 1. Is the result even or odd?
Answer: 7*3+1 = 22 so it’s even.
Tips: If they have trouble with remainders, or they tell you that 15/2 is 7.5, remind them that we want whole numbers only as the answer (here, 7) and if there is a leftover from the division (here, 1), we call it the Remainder.
step 3
Walk the Heroes through this concept now:
Consider the following operation on an arbitrary positive integer:
If the number is even, divide it by two.
If the number is odd, triple it and add one.
The Collatz Conjecture claims that no matter which positive number you start with, you will eventually reach 1, at which point you stop the operations. Because the numbers produced by these operations jump up and down like hailstones in the clouds, they are also called Hailstone Numbers!
Bakuage Co. Ltd., headquartered in Shibuya, Tokyo, announced on July 7, 2021, a prize of 120M JPY (about $1M) for anyone able to prove the Collatz Conjecture. Today we give it a shot.
Let’s start with 5 for example. If we follow the operations, we get:
5 → (3x5+1) = 16 → (16/2) = 8 → (8/2) = 4 → (4/2) = 2 → (2/2) = 1 in 5 operations
step 4
Ask the Hero(es) to find the length of the sequence of operations starting with the number 7.
They can keep notes on a piece of paper as they take turns with you, or one of their peers, computing each next number in the sequence until they reach 1
Answer: We start with 7 and apply the operators:
7 → (7x3+1) = 22 → (22/2) = 11 → (11x3+1) = 34 → (34/2) = 17 → (17x3+1) = 52 → (52/2) = 26 → (26/2) = 13 → (13x3+1) = 40 → (40/2) = 20 → (20/2) = 10 → (10/2) = 5 → (3x5+1) = 16 → (16/2) = 8 → (8/2) = 4 → (4/2) = 2 → (2/2) = 1
(This is a total of 16 steps - count the arrows - so the length of the sequence is 16)
