Adventure April 23 Math Monsters

The annual Lakamha Thonis joint festival, where important talks of diplomacy and trade are held during this three day event is in peril.

Monsters that normally live in the forest are coming close to Lakamha city and eating the crops: including the festival specialty. As members of the festival team, you have been tasked with dealing with the problem, so that the festival won't be cancelled (and the Thonisians won't look down on Lakamha).

The festival is in three days.
There may be 1-5 members on the team for this one shot.

The Plot

Stage 1: Protect Current Crops

Festival Organiser (FO) comes to the groups table during lunch break.
FO: "I need your help! Monsters have just eaten the outer crop field. They have pushed back into the forest by the guards, but we need to save the remaining field immidiately! We only have three days left and the food is needing to be served fresh!"

The team has been given X amount of fencing to build around the crops. Roll 4 d20 to determine the length of fencing.
They have also been given a map of the area.

by TaraFaeBelle

The team is asked to build the fences around the crops.
They are to use their math skills to work out the best area to fit the fence around as many crops as possible.
Find the dimensions of a rectangle with perimeter of the fence length above metres so that the area of the rectangle is a maximum. Either use calculus or trial and error to find the maximum area. The formulas for periemter and area of a rectangle are:

Once they have found the area they want to use, the team head to the crops and start building the fence.

If the crops form an area with dimensions of 20 m width and 10 m long, does the fencing cover the area? If not, does knowing that the cliff face is 2 m away from the crops, and can be used as part of the perimeter help?

Before they finish, three small Area Monsters come to try and eat the crops.

Options:

1. Fight the monsters!
2. Let monsters eat the crop.

Option 1

Once monsters are dead, finish the fence. Applauded by the FO - gain +1 to each damage from now on.

Option 2

If the fenced area doesn't cover all the crops, the monsters start eating from there. If the fenced area does cover all the crops, the monsters start eating from the edge of the crops. FO comes around and scolds the team, bringing in guards to help get rid of the monsters. Given a -1 to any damage from now on.

Stage 2: Investigate the Monsters

Two days are left before the festival. The team is now fully rested and any missing health is replenished. The FO comes to see the team again, tired and anxious, and asks them to work out where the monsters are coming from. The guards were up all night fighting off the monsters. They shouldn't be this far in, so there must be a reason why the monsters are trying to eat the Lakamhaan food and not the food in their forest home. 

The team's task is to find the monsters and work out why they are leaving their home space. The team can:

1. Talk to the guards.
2. Head straight to the forest.

Option 1

The guards from last night have trailed into the local tavern to eat before heading to sleep. Although tired, they tell of the type of monsters seen. Not just Area Monsters, but their evolved version: Volume Monsters. Multiply a single dice roll by 2 once per encounter.  

Option 2

Continue the adventure. No bonuses or penalties.

The team arrives at the forest entrance. There are a number of trails from many more monsters than usual in this season. There are 3 roads from the entrance leading into the forest. 
Roll a d20.

• For rolls below 10: no info. is found.
• For rolls 10 and above: the team remembers that trail 3 leads to the cliffs, nothing useful there. 
• For rolls 15 and above: the team remembers that trail 2 leads to where the monsters home is. 

Trail 1

The team arrives in a small glade. The trail does not continue after the glade. This is not where the monsters home is found. There are 2 Area Monsters and one Volume monster.
However, after defeating the monsters, the team finds trails to most of the way through trail 2. Along this trail, a bush is seen to have been avoided by the trails. Each member of the team can take one branch: throwing this at a monster who attacked them (as a reaction) allows them to divert the attack.

Trail 2

Along this trail, a bush is seen to have been avoided by the trails. Each member of the team can take one branch: throwing this at a monster who attacked them (as a reaction) allows them to divert the attack.

Further along the trail, there is another, similar but smaller bush that has been avoided by the monsters. Each member of the team can take one branch: throwing this at a monster who attacked them (as a reaction) allows them to divert most of the attack, such that they only get -1 damage (regardless of the monsters roll).

Most of the way through here, is another small glade, though the monsters home can be seen from the other side. (End of this trail is where the monsters home is.) If the team chose trail 1, they are to enter trail 3 from here.
There are 3 Volume monsters and 2 area monsters.

Once the monsters are defeated, the team continues to the monsters home. They hear a loud crunching, and see that a large, Corrupted Monster is eating an Area Monster. This monster is 5 times as big as a Volume Monster and seems to have displaced most of the smaller monsters from their usual home in and around the caves found here.

Trail 3

The team heads through the forest trail to the cliffs. There are no clues.

Before leaving the cover of the forest, they hear the screech of a large bird. It is not related to any of the monsters causing problems with the upcoming festival. Seeing the cliff through the leaves, they have the option to turn around or keep going and fight the bird monster.

Go back to forest entry.

After seeing the corrupted monster, the team knows that this is the issue. Head back to the FO and them about it.

Stage 3: Confront the Issue

The festival is tomorrow. The team is now fully rested and any missing health is replenished. The FO calls you over. There are a number of guard and hunters ready to defeat the corrupted beast the team found yesterday. Roll d6 + 4 for the amount of guards.

FO: "Please lead the hunting group to where you found the monster yesterday."
The FO also hands each person a one-use only shield to prevent any damage. "Use it wisely."

The team heads out to the forest entrance and meets the hunting team.
They head into the forest. Roll percentil die.

For anything less than 35, the team forgets what pathway they took. The team leads everyone to the cliffs where a(nother) bird monster is. The team has to fight the bird monster. On the way back to forest entrance, 1 of the guards gets distracted by an animal and gets separated from the group. -1 guard. Head to right trail.

If everyone rolls 35 or over, the team leads the hunting party to where they last saw the corrupted monster.

There are 20 Area Monsters running towards the group. The Hunters and Guards step and start to defeat them.

Does the team:

1. Help battle the Area Monsters
2. Wait at the back / Try to head home after having finished their job

Option 1

For every Area Monster the team defeats, 4 others are defeated by the Hunter Group. Thus, the team is to defeat 4 Area Monsters.

Option 2

A small group of 3 Volume Monsters come from trail 1, blocking the path home. Team is to defeat the 3 monsters.

After the monsters are defeated, a roar comes out of caves. This is the corrupted monster. It runs out of the cave and they throw a boulder.

d20 to dodge:

20 = you roll out of the way, and find another branch that can avert 1 monster attack.

10 or above = dodged out of the way, no damage.

5-9 = just scratched. -1 HP

2-4 = stumbled while getting away. Lose 1 attack point per roll.

1 = you try to dodge, but end up pushing one of the Hunters under the boulder. They are dead. You also suffer -2HP for landing on your elbow.

The hunters and guards head to deal with the monster. One of them sees a small pathway that leads above the caves the corrupted monster is outside of. They ask the team to follow the pathway and provide support from above.

The team follows the pathway.

By the time they reach the top, 2 of the Hunter group have fallen down. -2 guards from the Hunting Party.

Battle the Corrupted Monster.

For every 2 rounds of the team's turn, one of the remaining hunter team gets knocked out.
Each round, a Hunter/Guard will deal 10 damage to the monster.
The moster hits with two attacks at once - one to the team, one to the Hunter/Guard group.

Once the corrupted monster is defeated, take any remaining guards/hunters and go back to the FO.

He awards the team and the food for the festival is safe. (The more guards there are with the team, the more rewards the team gets). The team gets to finish work early and enjoy as much food as wanted during the 3 day festival.

They may even catch a glimpse of Vaneesa the Apocethary heading to the forest with her apprentice, Itotia to heal up any of the defeated guards/hunters.

Playable Characters:

Planner

HP: 70+d10
Skill: Instead of attacking as a turn, they may heal one person for d20 HP.

by AvalonCollierArt

Painter

HP: 75+d6
They may dodge any attack. By doing so they forfeit their next attack.

by AvalonCollierArt

Labourer

HP: 78
Skill: They may shield either themselves or someone else from any damage taken that round. By doing so, they forfeit their next attack.

by AvalonCollierArt (and then badly recoloured by TFB)

Monsters

Area Monster

HP: 50
Attack: d8
These monsters are damaged by area formulas.
To damage: Roll a d4 to determine which output each person will give. (If someone doesn't know calculus, rolling 1 and 3 = option 3; rolling 2 and 4 = option 4)
1. Integration

Find:

Roll for variables:

d4 for a

-d4 for b

d12 for c

d6 for d

Substitute the values rolled into the formula and solve for the area. The value for area becomes the damage given to the Area Monster chosen.

2. Trapeziodal Rule

The formula for the trapezoidal rule is:

Roll for variables:

d8/2 for height (h)

d6 for f(a)

d4 for f(b)

d6 for f(x₁)

by TaraFaeBelle

Substitute the values rolled into the formula and solve for the area. The value for area becomes the damage given to the Area Monster chosen.

3. Rectangle Area

The formula for the area of a rectangle is:

Roll for variables:

d4 for length (l)

d6 for width (w)

Substitute the values rolled into the formula and solve for the area. The value for area becomes the damage given to the Area Monster chosen.

4. Triangle Area

The formula for the area of a triangle is:

Roll for variables:

d4 for breadth (b)

d6 for height (h)

Substitute the values rolled into the formula and solve for the area. The value for area becomes the damage given to the Area Monster chosen.

by TaraFaeBelle

Volume Monster

Evolution of the Area Monster.
HP: 70
Attack: d10
Volume Monsters are damaged by integration and volume formulas.
To damage: Roll a d4 to determine which output each person will give. (If someone doesn't know calculus, rolling 1 and 2 = option 2; rolling 3 = option 3 and rolling 4 = option 4)
1. Integration

Find the area between:

Roll for variables:

d6 for a

Substitute the values rolled into the formula and solve for the area. The value for area becomes the damage given to the Volume Monster chosen.

2. Sphere

The formula for the volume of a sphere is:

Roll for variables:

d8 for radius (r)

Substitute the values rolled into the formula and solve for the volume. The value for volume becomes the damage given to the Volume Monster chosen, rounded to the nearest unit

3. Rectangular Prism

The formula for the volume of a rectangular prism is:

Roll for variables:

d4 for length (l)

d6 for width (w)

d8 for height (h)

Substitute the values rolled into the formula and solve for the volume. The value for volume becomes the damage given to the Volume Monster chosen.

4. Cone

The formula for the volume of a cone is:

Roll for variables:

d4 for radius (r)

d10 for height (h)

Substitute the values rolled into the formula and solve for the volume. The value for volume becomes the damage given to the Volume Monster chosen, rounded to the nearest unit.

by TaraFaeBelle

Bird Monster

HP: 90
Attack: d10*d4
These monsters are damaged by differentiation formulas.
To damage: Roll a d4 to determine which output each person will give. (If players don't know calculus, don't roll the d4 and just use option 4.)
1. Differentiation

Differentiate the following

Roll for variables:

d4 for a

Evalution the derivative when x=2. The value calculated becomes the damage given to the Bird Monster.

2. Product Rule

Differentiate the following

Roll for variables:

d4 for a

d8 for b

d4 for c

Evalution the derivative when x=2. The value calculated becomes the damage given to the Bird Monster.

3. Quotient Rule

Differentiate the following

Roll for variables:

d4 for a

d10 for b

d10 for c

Evalution the derivative when x=2. The value calculated becomes the damage given to the Bird Monster.

4. Subtraction

Simplify the following subtraction:

Roll for variables:

d4 for a

d4 for b

d12 for c

d6 for d

Substitute the values rolled into the formula and simplfy. The value calculated becomes the damage given to the Bird Monster.

Corrupted Monster

HP: 150
Attack: d20
These monsters are damaged by functions and graphing.
To damage: Roll a d4 to determine which output each person will give. (If players don't know calculus, rolling 1 and 2 = option 2; rolling 3 = option 3 and rolling 4 = option 4)
1. Gradient of tangent

Find the gradaient of the tangent to the curve

where x=1. Roll for variables:

d6 for a

Substitute the values rolled into the formula and solve for the gradient. The value for gradient becomes the damage given to the Corrupted Monster, rounded to the nearest unit.

2. Gradient

Find the gradient of the line that passes through the points (a, b) and (c, d). The formula for the gradient is

Roll for variables:

d6 for a

d8 for b

d10 for c

d4 for d

Substitute the values rolled into the formula and solve for the gradient. The absolute value for the gradient becomes the damage given to the Corrupted Monster, rounded to the nearest unit.

3. Linear Relationship

The gradient-intercept formula of a linear line is

Roll for variables:

d20 for y

d4 for m

d4 for c

Substitute the values rolled into the formula and solve for x. The absolute value for x becomes the damage given to the Corrupted Monster, rounded to the nearest unit.

4. Exponential Growth

The population growth of Area Monsters is usually found by the following formula:

Roll for variables:

d8 for a

d6 for b

Substitute the values rolled into the formula and solve for P. The value for P becomes the damage given to the Corrupted Monster, rounded to the nearest unit.