find rules（小学奥数）

main.rb

module HappyMath
  class FullPermutationRepeat
    include Enumerable

    def initialize(args, n)
      @args = args
      @n = n
    end

    def each(&b)
      _helper = ->(ret, n, args, &b) {
        if n == 0
          yield ret
        else
          args.each do |a|
            _helper.call(ret + [a], n - 1, args, &b)
          end
        end
      }

      _helper.call([], @n, @args, &b)
    end
  end

  class FullPermutation
    include Enumerable

    def initialize(args, n = args.size)
      @args = args
      @n = n
    end

    def each(&b)
      _helper = ->(ret, n, args, &b) {
        if n == 0
          yield ret
        else
          args.each do |a|
            _helper.call(ret + [a], n - 1, args - [a], &b)
          end
        end
      }

      _helper.call([], @n, @args, &b)
    end
  end

  Add = -> { _1 + _2 }
  Sub = -> { _1 - _2 }
  Mul = -> { _1 * _2 }
  Div = -> { _1 / _2 }
  ElementaryArithmetic = [Add, Sub, Mul, Div]

  Identity = -> { _2 }
  Evaluate = ->(a, args, calcs) {
    [Identity].concat(calcs).zip(args).reduce(nil) { |ret, pair|
      pair.first.call(ret, a[pair.last])
    }
  }

  class Solution
    include Enumerable

    def initialize(vars, result, functions)
      @vars = vars
      @result = result
      n = @vars.size
      @args_iterator = FullPermutation.new(n.times.to_a)
      @calcs_iterator = FullPermutationRepeat.new(functions, n - 1)
    end

    def each(&b)
      @args_iterator.each do |args|
        @calcs_iterator.each do |calcs|
          if Evaluate.call(@vars, args, calcs) == @result
            yield args, calcs
          end
        end
      end
    end
  end

  FindRules = ->(conditions) {
    ->(vars) {
      conditions.collect(&-> { Solution.new(*_1, ElementaryArithmetic) })
        .map(&:to_a).reduce(&:&)
        .collect(&-> { Evaluate.call(vars, *_1) })
    }
  }
end

conditions = [] << [[4, 3, 4], 24] << [[6, 5, 2], 40]
vars = [2, 3, 5]

p HappyMath::FindRules[conditions][vars].uniq

question.md

Question

find ? and get to make these statements correct:

get 24 by 4, 3, 4
get 40 by 6, 5, 2
get ?  by 2, 3, 5

where get is a function with only Elementary Arithmetics.

Answer

21