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Message: [QUOTE="Daniel Martin, post: 4525944"] And here's my narray-based solution to find the happiest number under 1_000_000 - it's not the shortest solution I've seen, but it's pretty fast. It eliminates numbers that end up in loops by setting all looping numbers to 0. #!/usr/bin/env ruby require 'narray' def dodigsum(initial, base) ndigits = (Math.log(initial.max)/Math.log(base)).ceil tmp = initial / (base ** NArray.to_na((0...ndigits).map{|x|[x]})) tmp = tmp % base tmp.mul!(tmp) initial.fill!(0).add!(tmp.sum(1)) end limit = ARGV[0] || 1_000_000 base = ARGV[1] || 10 limit = limit.to_i base = base.to_i check = NArray.int(limit + 1).indgen! check_initial = check.dup check_initial[1] = 0 dodigsum(check, base) checkp = check.dup onemask = check.eq(1) # onemask now contains the location of "0 order" happy numbers order = 0 found_ex = nil while (check.ge(2).count_true > 0) do check.mul!(check.ne(check_initial)) check = check[checkp] newmask = check.eq(1) order = order + 1 if (not newmask == onemask) found_ex = [newmask.gt(onemask).where.min, order] end onemask = newmask end puts "Happiest is #{found_ex[0]}, with happiness order #{found_ex[1]}" __END__ [/QUOTE]