Three seed numbers go in. Algebra runs. A team name comes out. Hit Generate and read the math trail below.
x
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y
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z
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Your robot team name will appear here
Adjective
Animal
Number
How the math works
Walk through each step. See exactly how algebra picks each piece of your team name.
Step 1 of 4
Start with random seed numbers
The generator picks three integers: x, y, and z. Each is a random whole number between 1 and 10. These are your variables — the raw inputs that drive everything else.
Step 2 of 4
Find the adjective using a linear equation
Plug x and y into a = 2x + y − 1 to get a number. Then use that number to look up word number a in the adjectives list.
This is called a linear equation because neither variable is squared or multiplied together — every term is just a variable times a constant. If you graphed every (x, y) pair that produces the same value of a, you'd get a straight line.
The numbers in front of x and y are called coefficients. They control how much each variable affects the result:
x has coefficient
2
Every time x goes up by 1, a goes up by 2. x has the bigger impact.
y has coefficient
1
Every time y goes up by 1, a goes up by 1. Half the impact of x.
The − 1 at the end is a constant. It shifts every result down by 1 regardless of what x and y are. Without it, the smallest possible output would be 2(1) + 1 = 3. With it, the smallest is 2. That small shift spreads results more evenly across the low end of the list.
Why does the result always land on a real word?
The adjective list has 26 words, numbered 0 to 25. x goes up to 10 and y goes up to 10, so the biggest possible value of a is 2(10) + 10 − 1 = 29. That is too high — index 29 does not exist in the list.
To fix this, the generator uses a mod , which gives the remainder after dividing by . So if a = 29, then 29 mod = , and that index lands on a real word.
Step 3 of 4
Find the animal using substitution
Take the adjective result a and substitute it into b = (a + z) mod . Mod keeps b between 0 and 11 no matter how large a gets. There are exactly 12 animals in the list, so every value of b lands on one.
Step 4 of 4
Build the team number
The team number comes from n = 3z² − x. Square z first, multiply by 3, then subtract x. Larger z values produce bigger numbers, giving elite teams four-digit names.
Key concept: Variables let us write one rule that works for any input. Change x or y and you get a different adjective, but the equation stays the same.
Control the variables yourself
Drag a slider and watch the name and equations update instantly.
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set the sliders below
a = 2x + y − 1
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adjective index (a mod 26)
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b = (a + z) mod 12
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n = 3z² − x
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Coefficient 2 — bigger impact on adjective
5
Coefficient 1 — smaller impact on adjective
3
Picks the animal + dominates the team number
4
Edit the word lists
Add or remove words — watch the mod equations update in the calc above
Notice + wonder
The equations use mod to keep results inside the word lists. The divisor comes directly from the list length — it is not a fixed number. Try adding or removing words, then look at the equations.
What changed in the mod equation when you added a word?
Does the name change even if you keep the sliders in the same position? Why?
What would happen if you had only 1 word in a list?
Your challenge
Set x = 2, y = 5, z = 3. What is the value of n? Work it out on paper using order of operations, then check your answer.
n = 3(3²) − 2 = 3(9) − 2 = 27 − 2 = 25
Square z first. Then multiply by 3. Then subtract x. The team number is 25.