### thanhchauns2's blog

By thanhchauns2, history, 14 months ago,

Hi, I collected the solutions for the problems of April Fools Day Contest 2023. Before the official editorial being posted, we can discuss about the problems here.

P/s: The editorial was published.

1812A - Are You a Robot?

Solution

1812B - Was it Rated?

Solution

1812C - Digits

Solution

1812D - Trivial Conjecture

Solution

1812E - Not a Geometry Problem

Solution

1812F - Factorization

Solution

1812G - Colour Vision

Solution

1812H - Expected Twist

Solution

1812I - Mountain Climber

Solution

1812J - Unmysterious Language

Solution
• +28

 » 14 months ago, # |   +8 After about 300 — 400 steps, a positive number will be decreased down to 1. Where did you get those numbers from? the conjecture asks whether every positive integer will eventually get to 1 by applying the operation however many times you'd like.The biggest answer allowed (103 digits) will take more than 3,000 operations to reach 1, but it might take millions, or never reach 1 (proving the conjecture false), which means that the [REDACTED] part must be pretty small, or the grader wouldn't be able to evaluate a very large submission definitively.
•  » » 14 months ago, # ^ |   0 Here. Or I could remember the wrong number, I watched it a long time ago.
•  » » » 14 months ago, # ^ |   0 I think it is around $350$: void solve(){ int mx = 0; for (int n1 = 1; n1 < 100000; n1++){ int steps = 0; for (int n = n1; n != 1; steps++){ if (n & 1) n = 3 * n + 1; else n /= 2; } mx = max(mx, steps); } cout << mx << '\n'; } 
•  » » » » 14 months ago, # ^ |   0 That's for numbers up to 1e5, we're talking about numbers up to 1e1000
•  » » 14 months ago, # ^ |   0 I believe the grader can just simulate $10^5$ ish steps to check if an answer is valid or not. In testing, the best number I could find was around $2.5 \cdot 10^4$ steps by just randomly generating $1000$ digit numbers and running them. In any event, it is probably impossible to find a positive integer that could work on the given constraints, and if you could, you could probably write a paper on it!