prob_32.rb

#!/usr/bin/env ruby

# Let D(a) be the # digits of a
#    e.g., D(100) = 3, D(999) = 3, D(2) = 1
#
# Here are the requirements by the problem
# 1. a * b == c
# 2. D(a) + D(b) + D(c) == 9
#
# From 1. we can derive that D(c) is either D(a)+D(b) or D(a)+D(b)-1
# Hence, we know that D(a)+D(b) must be 5, which limits the searching range
# That is, [D(a), D(b)] is [1, 4] or [2, 3]

require "MyInteger"

def search dA, dB
	(10**(dA-1)...10**dA).each {|a|
		next if a.zeroInDigits or a.hasDigitInDuplicate
		(10**(dB-1)...10**dB).each {|b|
			if b.zeroInDigits or b.hasDigitInDuplicate or a.hasSameDigitAs b
				next
			else
				c = a*b
				break if c.to_s.length>4
				next if c.zeroInDigits or c.hasDigitInDuplicate or a.hasSameDigitAs c or b.hasSameDigitAs c
				@products[c] = true
			end
		}
	}
end

@products = Hash.new
search 1, 4
search 2, 3
sum = 0
@products.each {|product, valueTF| sum += product}
puts sum