diff --git a/extra/project-euler/051/051.factor b/extra/project-euler/051/051.factor
index b42a491e3c..ff45e9e58a 100644
--- a/extra/project-euler/051/051.factor
+++ b/extra/project-euler/051/051.factor
@@ -1,38 +1,60 @@
 ! Copyright (C) 2009 Jon Harper.
 ! See http://factorcode.org/license.txt for BSD license.
+
+! http://projecteuler.net/index.php?section=problems&id=1
+
+! DESCRIPTION
+! -----------
+
+
+! By replacing the first digit of *3, it turns out that
+! six of the nine possible values:
+! 13, 23, 43, 53, 73, and 83, are all prime.
+! By replacing the third and fourth digits of 56**3 with the same digit,
+! this 5-digit number is the first example having seven primes among
+! the ten generated numbers, yielding the family:
+! 56003, 56113, 56333, 56443, 56663, 56773, and 56993.
+! Consequently 56003, being the first member of this family,
+! is the smallest prime with this property.
+! 
+! Find the smallest prime which, by replacing part of the number
+! (not necessarily adjacent digits) with the same digit,
+! is part of an eight prime value family.
+
+! SOLUTION
+! --------
+
+! for each prime number, count the families it belongs to. When one reaches count of 8, stop, and get the smallest number by replacing * with ones.
+
 USING: assocs kernel math math.combinatorics math.functions
 math.parser math.primes namespaces project-euler.common
-sequences sets strings grouping math.ranges arrays ;
+sequences sets strings grouping math.ranges arrays fry math.order ;
 IN: project-euler.051
-
+<PRIVATE
 SYMBOL: family-count
 SYMBOL: large-families
 : reset-globals ( -- ) 
     H{ } clone family-count set
     H{ } clone large-families set ;
 
-: append-or-create ( value seq/f -- seq )
-    dup [ swap suffix ] [ drop 1array ] if ;
-: append-at ( value key assoc -- )
-    [ at append-or-create ] 2keep set-at ;
-: digits-positions ( str -- positions )
-    H{ } clone swap over [ swapd append-at ] curry each-index ;
+: digits-positions ( str -- positions ) 
+    H{ } clone [ '[ swap _ push-at ] each-index ] keep ;
 
 : *-if-index ( char combination index -- char )
     member? [ drop CHAR: * ] when ;
 : replace-positions-with-* ( str positions -- str )
     [ *-if-index ] curry map-index ;
-: all-size-combinations ( seq -- combinations )
+: all-positions-combinations ( seq -- combinations )
     dup length [1,b] [ all-combinations ] with map concat ;
 
 : families ( stra -- seq )
     dup digits-positions values 
-    [ all-size-combinations [ replace-positions-with-* ] with map ] with map concat ;
+    [ all-positions-combinations [ replace-positions-with-* ] with map ] with map concat ;
 
 : save-family ( family -- )
-    family-count get dupd at 8 = [ large-families get conjoin ] [ drop ] if ;
+    dup family-count get at 8 = [ large-families get conjoin ] [ drop ] if ;
 : increment-family ( family -- )
-    family-count get dupd at* [ 1 + ] [ drop 1 ] if swap family-count get set-at ;
+   family-count get inc-at ;
 : handle-family ( family -- )
     [ increment-family ] [ save-family ] bi ;
 
@@ -52,7 +74,11 @@ SYMBOL: large-families
 : (euler051) ( i -- answer )
     dup test-n-digits-primes 
     dup assoc-size 0 > 
-    [ nip values [ fill-*-with-ones string>number ] map infimum ]
+    [ nip values [ fill-*-with-ones string>number ] [ min ] map-reduce ]
     [ drop 1 + (euler051) ] if ;
+PRIVATE>
+
 : euler051 ( -- answer )
     2 (euler051) ;
+
+SOLUTION: euler051