> For the complete documentation index, see [llms.txt](https://digitalgarden.batamladen.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://digitalgarden.batamladen.com/writeups/ctfs/pascal-ctf-2026/crypto-ice-creamer.md).

# Crypto - Ice Creamer

Description:\
Elia’s swamped with algebra but craving a new ice-cream flavor, help him crack these equations so he can trade books for a cone!

`nc cramer.ctf.pascalctf.it 5002`<br>

We have main.py from the chall.

```python
import os
from random import randint

def generate_variable():
    flag = os.getenv("FLAG", "pascalCTF{REDACTED}") # The default value is a placeholder NOT the actual flag
    flag = flag.replace("pascalCTF{", "").replace("}", "")
    x = [ord(i) for i in flag]
    return x

def generate_system(values):
    for _ in values:
        eq = []
        sol = 0
        for i in range(len(values)):
            k = randint(-100, 100)
            eq.append(f"{k}*x_{i}")
            sol += k * values[i]

        streq = " + ".join(eq) + " = " + str(sol)
        print(streq)


def main():
    x = generate_variable()
    generate_system(x)
    print("\nSolve the system of equations to find the flag!")

if __name__ == "__main__":
    main()
```

When nc to the challenge we get a long output of equations.

<figure><img src="/files/LB8CUalUGAAo8aQlfoKl" alt=""><figcaption></figcaption></figure>

plan for this challenge was to:\
\- Copy the equations from the server output\
\- Build matrix A (coefficients) and vector b (right-hand side)\
\- Solve the linear system\
\- Convert each solution x\_i to a character\
\- Wrap the result in pascalCTF{}

#### Solve.py

```
import re
import numpy as np

equations = open("equations.txt").read().strip().splitlines()

A = []
b = []

for line in equations:
    left, right = line.split("=")
    b.append(int(right.strip()))

    coeffs = [0] * 28
    terms = left.split("+")
    for t in terms:
        k, var = t.strip().split("*")
        idx = int(var.replace("x_", ""))
        coeffs[idx] = int(k)

    A.append(coeffs)

A = np.array(A, dtype=np.int64)
b = np.array(b, dtype=np.int64)

# Solve system
x = np.linalg.solve(A, b)
x = [int(round(v)) for v in x]

flag = "".join(chr(v) for v in x)
print("pascalCTF{" + flag + "}")
```

Note: THe server output was first put in a file "equations.txt".

FLAG:

pascalCTF{0h\_My\_G0DD0\_too\_much\_m4th\_:O}


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://digitalgarden.batamladen.com/writeups/ctfs/pascal-ctf-2026/crypto-ice-creamer.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.