From b25b4532a45698e235c387e32d8ed27810352342 Mon Sep 17 00:00:00 2001
From: Jonathan Chan <jonathanhwchan@gmail.com>
Date: Mon, 5 Dec 2016 20:35:58 -0800
Subject: [PATCH] Problem 38

---
 38     | Bin 0 -> 8256 bytes
 38.c   |  57 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 38.txt |  27 +++++++++++++++++++++++++++
 3 files changed, 84 insertions(+)
 create mode 100755 38
 create mode 100644 38.c
 create mode 100644 38.txt

diff --git a/38 b/38
new file mode 100755
index 0000000000000000000000000000000000000000..fa518d437d2e39d0a807efe9723ff780894d838a
GIT binary patch
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diff --git a/38.c b/38.c
new file mode 100644
index 0000000..5657510
--- /dev/null
+++ b/38.c
@@ -0,0 +1,57 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdbool.h>
+
+bool hasUniqueDigits (int i) {
+    int a = i % 10;
+    i /= 10;
+    int b = i % 10;
+    i /= 10;
+    int c = i % 10;
+    i /= 10;
+    int d = i % 10;
+    return  a != b && a != c && a != d &&
+            b != c && b != d &&
+            c != d;
+}
+
+bool isPandigital (int i, int j) {
+    int a = i % 10;
+    i /= 10;
+    int b = i % 10;
+    i /= 10;
+    int c = i % 10;
+    i /= 10;
+    int d = i % 10;
+    
+    int e = j % 10;
+    j /= 10;
+    int f = j % 10;
+    j /= 10;
+    int g = j % 10;
+    j /= 10;
+    int h = j % 10;
+    j /= 10;
+    int k = j % 10;
+
+    return  a != 0 && b != 0 && c != 0 && d != 0 && e != 0 && f != 0 && g != 0 && h != 0 && k != 0 &&
+            a != b && a != c && a != d && a != e && a != f && a != g && a != h && a != k &&
+            b != c && b != d && b != e && b != f && b != g && b != h && b != k &&
+            c != d && c != e && c != f && c != g && c != h && c != k &&
+            d != e && d != f && d != g && d != h && d != k &&
+            e != f && e != g && e != h && e != k &&
+            f != g && f != h && f != k &&
+            g != h && g != k && 
+            h != k;
+}
+
+int main () {
+    int n = 9182;
+    for (int i = 9183; i <= 9876; i++) {
+        if (hasUniqueDigits (i)) {
+            if (isPandigital (i, 2 * i))
+                n = i;
+        }
+    }
+    printf ("%d%d\n", n, 2 * n);
+}
diff --git a/38.txt b/38.txt
new file mode 100644
index 0000000..3862fae
--- /dev/null
+++ b/38.txt
@@ -0,0 +1,27 @@
+Given a certain tuple (1, 2, ..., n), only a certain range of integers i are allowed to produce a nine-digit concatenation.
+(1, 2):             1 * _ _ _ _ = _ _ _ _
+                    2 * _ _ _ _ = _ _ _ _ _
+                        5000 <= i <= 9999
+(1, 2, 3):          1 * _ _ _ = _ _ _
+                    2 * _ _ _ = _ _ _
+                    3 * _ _ _ = _ _ _
+                        100 <= i <= 333
+(1, 2, 3, 4):       1 * _ _ = _ _
+                    2 * _ _ = _ _
+                    3 * _ _ = _ _
+                    4 * _ _ = _ _ _
+                        25 <= i <= 33
+(1, 2, 3, 4, 5):    1 * _ = _
+                    2 * _ = _ _
+                    3 * _ = _ _
+                    4 * _ = _ _
+                    5 * _ = _ _
+                        5 <= i <= 9
+(1, 2, 3, 4, 5, 6): 1 * _ = _
+                    2 * _ = _
+                    3 * _ = _
+                    4 * _ = _ _ 
+                    5 * _ = _ _
+                    6 * _ = _ _
+                        i == 3
+In the given example, 9 x (1, 2, 3, 4, 5) = 918273645. Then to produce a larger concatenation, with the given restrictions on i, we can only use i x (1, 2), where 9183 <= i <= 9876. Then only 693 values of i need to be tested.