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problem 67 · 9 lines

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<p>By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.</p>
<p class="monospace center"><span class="red"><b>3</b></span><br/><span class="red"><b>7</b></span> 4<br/>
2 <span class="red"><b>4</b></span> 6<br/>
8 5 <span class="red"><b>9</b></span> 3</p>
<p>That is, 3 + 7 + 4 + 9 = 23.</p>
<p>Find the maximum total from top to bottom in <a href="resources/0067_triangle.txt">triangle.txt</a> (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.</p>
<p class="smaller"><b>NOTE:</b> This is a much more difficult version of <a href="problem=18">Problem 18</a>. It is not possible to try every route to solve this problem, as there are $2^{99}$ altogether! If you could check one trillion ($10^{12}$) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)</p>
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