Solution to Project Euler problem 206

extra/project-euler/206/206-tests.factor

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+USING: project-euler.206 tools.test ;
+IN: project-euler.206.tests
+
+[ 1389019170 ] [ euler206 ] unit-test

extra/project-euler/206/206.factor

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+! Copyright (c) 2010 Aaron Schaefer. All rights reserved.
+! The contents of this file are licensed under the Simplified BSD License
+! A copy of the license is available at http://factorcode.org/license.txt
+USING: grouping kernel math math.ranges project-euler.common sequences ;
+IN: project-euler.206
+
+! http://projecteuler.net/index.php?section=problems&id=206
+
+! DESCRIPTION
+! -----------
+
+! Find the unique positive integer whose square has the form
+! 1_2_3_4_5_6_7_8_9_0, where each “_” is a single digit.
+
+
+! SOLUTION
+! --------
+
+! Through mathematical analysis, we know that the number must end in 00, and
+! the only way to get the last digits to be 900, is for our answer to end in
+! 30 or 70.
+
+<PRIVATE
+
+! 1020304050607080900 sqrt, rounded up to the nearest 30 ending
+CONSTANT: lo 1010101030
+
+! 1929394959697989900 sqrt, rounded down to the nearest 70 ending
+CONSTANT: hi 1389026570
+
+: form-fitting? ( n -- ? )
+    number>digits 2 group [ first ] map
+    { 1 2 3 4 5 6 7 8 9 0 } = ;
+
+: candidates ( -- seq )
+    lo lo 40 + [ hi 100 <range> ] bi@ append ;
+
+PRIVATE>
+
+: euler206 ( -- answer )
+    candidates [ sq form-fitting? ] find-last nip ;
+
+! [ euler206 ] 100 ave-time
+! 321 ms ave run time - 8.33 SD (100 trials)
+
+SOLUTION: euler206