Merge pull request #1225 from noudald/challenge-046-noud

Challenge 046 noud

3 files changed, 97 insertions, 0 deletions

diff --git a/challenge-046/noud/blog.txt b/challenge-046/noud/blog.txt
new file mode 100644
index 0000000000..d1fa9a7ad0
--- /dev/null
+++ b/challenge-046/noud/blog.txt
@@ -0,0 +1 @@
+https://www.noudaldenhoven.nl/wordpress/?p=288
diff --git a/challenge-046/noud/raku/ch-1.p6 b/challenge-046/noud/raku/ch-1.p6
new file mode 100644
index 0000000000..8d77c8ade8
--- /dev/null
+++ b/challenge-046/noud/raku/ch-1.p6
@@ -0,0 +1,55 @@
+# Cryptic Message
+#
+# The communication system of an office is broken and message received are not
+# completely reliable. To send message Hello, it ended up sending these
+# following:
+#
+# H x l 4 !
+# c e - l o
+# z e 6 l g
+# H W l v R
+# q 9 m # o
+#
+# Similary another day we received a message repeatedly like below:
+#
+# P + 2 l ! a t o
+# 1 e 8 0 R $ 4 u
+# 5 - r ] + a > /
+# P x w l b 3 k \
+# 2 e 3 5 R 8 y u
+# < ! r ^ ( ) k 0
+#
+# Write a script to decrypt the above repeated message (one message repeated 6 times).
+# HINT: Look for characters repeated in a particular position in all six messages received.
+
+sub select-double(@a) {
+    for @a -> $elm {
+        if (@a.grep($elm).elems == 2) {
+            return $elm;
+        }
+    }
+}
+
+sub decrypt(@a) {
+    return [~] ([Z] @a).map({ select-double($_) });
+}
+
+my @enc1 = (
+    <H x l 4 !>,
+    <c e - l o>,
+    <z e 6 l g>,
+    <H W l v R>,
+    <q 9 m # o>);
+
+say decrypt(@enc1);
+
+
+my @enc2 = (
+    ('P', '+', '2', 'l', '!', 'a', 't', 'o'),
+    ('1', 'e', '8', '0', 'R', '$', '4', 'u'),
+    ('5', '-', 'r', ']', '+', 'a', '>', '/'),
+    ('P', 'x', 'w', 'l', 'b', '3', 'k', '\\'),
+    ('2', 'e', '3', '5', 'R', '8', 'y', 'u'),
+    ('<', '!', 'r', '^', '(', ')', 'k', '0'));
+
+say decrypt(@enc2);
diff --git a/challenge-046/noud/raku/ch-2.p6 b/challenge-046/noud/raku/ch-2.p6
new file mode 100644
index 0000000000..85131bb6c6
--- /dev/null
+++ b/challenge-046/noud/raku/ch-2.p6
@@ -0,0 +1,41 @@
+# Is the room open?
+#
+# There are 500 rooms in a hotel with 500 employees having keys to all the
+# rooms. The first employee opened main entrance door of all the rooms. The
+# second employee then closed the doors of room numbers 2,4,6,8,10 and so on to
+# 500. The third employee then closed the door if it was opened or opened the
+# door if it was closed of rooms 3,6,9,12,15 and so on to 500. Similarly the
+# fourth employee did the same as the third but only room numbers 4,8,12,16 and
+# so on to 500. This goes on until all employees has had a turn.
+#
+# Write a script to find out all the rooms still open at the end.
+
+
+# This took me a while to figure out.
+#
+# 1. Given a single room number N, how many times did an employee open or
+# closed the door of that room? Let's look at the k-th employee. The employee
+# opens or closes the door of room N if and only if k is a divisor of N. So if
+# we want to know how often the door has been opened or closed we must count
+# the number of divisors of the room number N.
+#
+# 2. If room number N has been opened or closed an even number of times the
+# door is closed. If the number of divisors of N is an odd number the door is
+# open. So this problem is equivalent to finding all N equal or below 500 that
+# have an odd number of divisors.
+#
+# 3. Take the prime decomposition of N:
+#
+#   N = p1^k1 * p2^k2 * ... * pi^ki.
+#
+# The number of divisors of N is (k1 + 1) * (k2 + 1) * ... * (ki + 1).
+#
+# 4. The number of divisors of N is odd if and only if k1, k2, ..., ki, are all
+# even. (If kj would be odd, kj + 1 is even, hence every product with kj + 1 is
+# even) But if k1, k2, ..., ki are all even, N is a squared number.
+#
+# 5. Therefore, the only open rooms can be rooms with a squared number below
+# 500. This is a (maybe difficult to understand why correct) one-liner.
+
+say "Open rooms:";
+say $_**2 for 1..(500.sqrt);