Re: challenge problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg61271] Re: [mg61219] challenge problem*From*: János <janos.lobb at yale.edu>*Date*: Fri, 14 Oct 2005 05:54:25 -0400 (EDT)*References*: <200510130539.BAA04503@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Oct 13, 2005, at 1:39 AM, Murray Eisenberg wrote: > At http://www.itasoftware.com/careers/eng/job1.php, there are a number > of interestng programming problems posed. One, the "Lucky Sevens", is > to write a program that will find the sum of all those integers > between > 1 and 10^11 that are divisible by 7 AND whose reversed-digit forms are > also divisible by 7. > > I should think that an elegant and possibly efficient solution in > Mathematica would be to use the form func /@ Range[10^11]. But since > Mathematica 5.2 on my my 32-bit Windows machine won't let me form > Range[10^11], a 64-bit architecture would seem to be required. > > > -- > Murray Eisenberg murray at math.umass.edu > Mathematics & Statistics Dept. > Lederle Graduate Research Tower phone 413 549-1020 (H) > University of Massachusetts 413 545-2859 (W) > 710 North Pleasant Street fax 413 545-1801 > Amherst, MA 01003-9305 Here is a newbie approach: n=8 In[30]:= Timing[Total[First[ Last[Reap[i = 7; maxi = 10^7; While[ i < maxi, If[Mod[FromDigits[ Reverse[ IntegerDigits[i]]], 7] == 0, Sow[i]]; i += 7]]]]]] Out[35]= {426.28709100000003*Second, 102184086890270} For n=11 it would take 5 and half days on my G4 :) Probably faster ways can be done if you code out the divisibility tests from http://mathworld.wolfram.com/DivisibilityTests.html and use them instead of Mod. I do not know how Mod is optimized for bigger numbers. János

**References**:**challenge problem***From:*Murray Eisenberg <murray@math.umass.edu>