From 0645ef2d2b3087289fcf54bdcce5df3e0e1904d7 Mon Sep 17 00:00:00 2001
From: Tilman Hoffbauer <tilman.hoffbauer@juforum.de>
Date: Fri, 16 Apr 2021 10:14:44 +0200
Subject: [PATCH] Add code

---
 .gitignore  |  1 +
 Cargo.lock  |  5 +++++
 Cargo.toml  |  9 +++++++++
 README.md   | 11 +++++++++++
 output.txt  | 29 +++++++++++++++++++++++++++++
 src/main.rs | 22 ++++++++++++++++++++++
 6 files changed, 77 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 Cargo.lock
 create mode 100644 Cargo.toml
 create mode 100644 README.md
 create mode 100644 output.txt
 create mode 100644 src/main.rs

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ea8c4bf
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+/target
diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 0000000..228fb3a
--- /dev/null
+++ b/Cargo.lock
@@ -0,0 +1,5 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+[[package]]
+name = "stellenteilerraetsel"
+version = "0.1.0"
diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..709a479
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,9 @@
+[package]
+name = "stellenteilerraetsel"
+version = "0.1.0"
+authors = ["Tilman Hoffbauer <tilman.hoffbauer@juforum.de>"]
+edition = "2018"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..6ffeac1
--- /dev/null
+++ b/README.md
@@ -0,0 +1,11 @@
+# Stellenteiler-Rätsel
+
+*Finde eine Zahl in einer Basis n, wo die erste Stelle sich durch 1, die erste und zweite Stelle durch 2, ..., die erste bis n-te Stelle sich durch n teilen lässt.*
+
+Lösung in Rust implementiert. Auf einem Ryzen 5 2700 mit 16 GB RAM getestet. Programmausführung per Cargo:
+
+```
+cargo run --release
+```
+
+Zur Installation von Rust siehe rustup.
diff --git a/output.txt b/output.txt
new file mode 100644
index 0000000..71b1a68
--- /dev/null
+++ b/output.txt
@@ -0,0 +1,29 @@
+Basis 2: [2]
+Basis 3: []
+Basis 4: [108, 228]
+Basis 5: []
+Basis 6: [13710, 44790]
+Basis 7: []
+Basis 8: [6996920, 11128712, 12306056]
+Basis 9: []
+Basis 10: [3816547290]
+Basis 11: []
+Basis 12: []
+Basis 13: []
+Basis 14: [7838911147538198]
+Basis 15: []
+Basis 16: []
+Basis 17: []
+Basis 18: []
+Basis 19: []
+Basis 20: []
+Basis 21: []
+Basis 22: []
+Basis 23: []
+Basis 24: []
+Basis 25: []
+Basis 26: []
+Basis 27: []
+Basis 28: []
+
+-- out of memory --
diff --git a/src/main.rs b/src/main.rs
new file mode 100644
index 0000000..f2fcfd2
--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,22 @@
+fn main() {
+    for base in 2..=64 {
+        println!("Basis {}: {:?}", base, solve(base));
+    }
+}
+
+fn solve(base: u128) -> Vec<u128> {
+    let digits: Vec<u128> = (0..base).collect();
+    let mut candidates = vec![(0, digits)];
+    for _ in 0..base {
+        candidates = candidates
+            .into_iter()
+            .flat_map(|(stumb, left)| left.clone().into_iter().map(move |digit| {
+                let mut next_left: Vec<u128> = left.clone();
+                next_left.retain(|d| *d != digit);
+                (stumb * base + digit, next_left)
+            }))
+            .filter(|(number, left)| number % (base - (left.len() as u128)) == 0)
+            .collect();
+    }
+    candidates.into_iter().map(|(number, _)| number).collect()
+}