# Challenges responses

First Challenge: The French Question

The secret text was encoded using the VIGENÈRE algorithm (the name of the person was a clue) using CHALLENGE as the key (another clue in the text). You can decode it by hand (using the table at https://en.wikipedia.org/wiki/Vigenère_cipher) or online at  https://www.dcode.fr/vigenere-cipher or https://planetcalc.com/2468/. After adding spaces you get the text below, in French:

NOUS AVONS BESOIN DES ONZE NUMÉROS DU NUMÉRO DE TÉLÉPHONE DE GLOBANT À NEW YORK

You can translate that using Google, and it means you need the eleven digits of the Globant phone number in New York, so the answer is 18772155230.

We have to find a ten-digit perfect square, so that picking four specific digits of it produces another perfect square. The JavaScript code I used to solve this is below:

const includesAllDigits = n => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9].every(d => n.includes(d));
const pick = (n, s) => s.split("").reduce((acc, c) => acc += n["REGULATION".indexOf(c)], "");
const MINRT = Math.ceil(Math.sqrt(123456789));
const MAXRT = Math.floor(Math.sqrt(9876543210));
for (let r = MINRT; r <= MAXRT; r++) {
let REGULATION = String(r * r);
if (REGULATION.length < 10) REGULATION = "0" + REGULATION;
if (includesAllDigits(REGULATION)) {
const RULE = pick(REGULATION, "RULE");
r2 = Math.sqrt(RULE);
if (r2 === Math.floor(r2)) {
console.log(r, REGULATION, r2, RULE, pick(REGULATION, "IGNOREALL"));
}
}
}

The output was 87639 7680594321 84 7056 381276955 so REGULATION=7680594321 (=876392), RULE=7056 (=842), and IGNORE ALL=381276955.

Third Challenge: The Mexican Squares

This is the "Eight Queens" problem in disguise -  and the German agent's name means "QUEEN OF CHESS", as an extra clue. The solution is 73025164.

Fourth Challenge: The Astronomy Details

Checking the flags of all the countries and the list, and remembering that the Sun (as in the flags of Antigua and Barbuda, Argentina, Bolivia, Costa Rica, Ecuador, and Uruguay) is a star, you get 19 countries, shown below. The flags were taken from Wikipedia.

The list is:

1. Antigua & Barbuda

2. Costa Rica

3. Cuba

4. The Commonwealth of Dominica

6. Honduras

7. Panama

8. The Federation of Saint Kitts and Nevis

9. The United States of America

10. Argentina

11. Bolivia

12. Brazil

13. Chile