-! Copyright (c) 2008 Eric Mertens
+! Copyright (c) 2008 Eric Mertens.
! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math math.functions sequences sequences.lib ;
-
+USING: kernel math math.functions sequences project-euler.common ;
IN: project-euler.148
+! http://projecteuler.net/index.php?section=problems&id=148
+
+! DESCRIPTION
+! -----------
+
+! We can easily verify that none of the entries in the first seven rows of
+! Pascal's triangle are divisible by 7:
+
+! 1
+! 1 1
+! 1 2 1
+! 1 3 3 1
+! 1 4 6 4 1
+! 1 5 10 10 5 1
+! 1 6 15 20 15 6 1
+
+! However, if we check the first one hundred rows, we will find that only 2361
+! of the 5050 entries are not divisible by 7.
+
+! Find the number of entries which are not divisible by 7 in the first one
+! billion (10^9) rows of Pascal's triangle.
+
+
+! SOLUTION
+! --------
+
<PRIVATE
: sum-1toN ( n -- sum )
- dup 1+ * 2/ ; inline
+ dup 1 + * 2/ ; inline
: >base7 ( x -- y )
- [ dup 0 > ] [ 7 /mod ] [ ] unfold nip ;
+ [ dup 0 > ] [ 7 /mod ] produce nip ;
: (use-digit) ( prev x index -- next )
- [ [ 1+ * ] [ sum-1toN 7 sum-1toN ] bi ] dip ^ * + ;
-
-PRIVATE>
+ [ [ 1 + * ] [ sum-1toN 7 sum-1toN ] bi ] dip ^ * + ;
: (euler148) ( x -- y )
>base7 0 [ (use-digit) ] reduce-index ;
-: euler148 ( -- y )
+PRIVATE>
+
+: euler148 ( -- answer )
10 9 ^ (euler148) ;
+
+! [ euler148 ] 100 ave-time
+! 0 ms ave run time - 0.17 SD (100 trials)
+
+SOLUTION: euler148