http://math.stackexchange.com/questions/1225690/how-many-solutions-can-the-2a3b4c5d6e-22-equation-have-if-a-b-c-d

eqn.rb

#!/usr/bin/env ruby

def check
  min = -32
  ma = 4  # 2^5 = 32 > 22
  mb = 2  # 3^3 = 27 > 22
  mc = 2  # 4^3 = 64 > 22
  md = 1  # 5^2 = 25 > 22
  me = 1  # 6^2 = 36 > 22
  puts "checking"
  puts "a in [#{min},..,#{ma}]"
  puts "b in [#{min},..,#{mb}]"
  puts "c in [#{min},..,#{mc}]"
  puts "d in [#{min},..,#{md}]"
  puts "e in [#{min},..,#{me}]"
  nc = (ma-min+1)*(mb-min+1)*(mc-min+1)*(md-min+1)*(me-min+1)
  puts "cases: #{nc}"
  nt = 0
  ns = 0
  for a in min..ma do
    pa = 2**a
    xa = pa
    for b in min..mb do
      pb = 3**b
      xb = xa + pb
      for c in min..mc do
        pc = 4**c
        xc = xb + pc
        for d in min..md do
          pd = 5**d
          xd = xc + pd
          for e in min..me do
            pe = 6**e
            xe = xd + pe
            x = xe
            nt += 1
            if x == 22
              ns += 1
              puts "#{ns}. (#{a},#{b},#{c},#{d},#{e}): #{pa}+#{pb}+#{pc}+#{pd}+#{pe}=#{x}"
            end
          end
        end
      end
    end
  end
  puts "number of tests: #{nt}"
  puts "number of solutions: #{ns}"
  return ns
end

check