title: Three Arrays and Subset Sum
body: <blockquote>
  <p>Array 1: 1 2 4 8 21</p>
  <p>Array 2: 3 5 6 7 19 20</p>
  <p>Array 3: 9 10 11 12 13 14 15 16 17 18</p>
  </blockquote>
  <p>There are 3 arrays.
  We are adding numbers starting from 1.
  If the number is equal to the sum of any subset, we can not add to it.</p>
  <p><strong>For example:</strong></p>
  <p>22 can not be added to any array.</p>
  <blockquote>
  <blockquote>
  <p>Because 1 + 21 = 22, 3 + 19 = 22, 10 + 12 = 22</p>
  </blockquote>
  </blockquote>
  <p>21 can not be added to array 2.</p>
  <blockquote>
  <blockquote>
  <p>Because 3 + 5 + 6 + 7 = 21</p>
  </blockquote>
  </blockquote>
  <p>7 can be added to array 2.</p>
  <blockquote>
  <blockquote>
  <p>Because (3 + 5 != 7), (3 + 6 != 7), (5 + 6 != 7), (3 + 5 + 6 != 7) ...</p>
  </blockquote>
  </blockquote>
  <p>Numbers should be added in order. (If I didn't add 22, I can't add 23)</p>
  <p><strong>21 is the greatest number what I can add.</strong></p>
  <p><strong>I want to add greater number.</strong></p>
  <p><strong>Is there a solution for this problem?</strong></p>
  <p><strong>What is proper name of this problem?</strong></p>
  <p>Thanks...</p>