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problem 18 · 24 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 of the triangle below:</p>
<p class="monospace center">75<br/>
95 64<br/>
17 47 82<br/>
18 35 87 10<br/>
20 04 82 47 65<br/>
19 01 23 75 03 34<br/>
88 02 77 73 07 63 67<br/>
99 65 04 28 06 16 70 92<br/>
41 41 26 56 83 40 80 70 33<br/>
41 48 72 33 47 32 37 16 94 29<br/>
53 71 44 65 25 43 91 52 97 51 14<br/>
70 11 33 28 77 73 17 78 39 68 17 57<br/>
91 71 52 38 17 14 91 43 58 50 27 29 48<br/>
63 66 04 68 89 53 67 30 73 16 69 87 40 31<br/>
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23</p>
<p class="note"><b>NOTE:</b> As there are only $16384$ routes, it is possible to solve this problem by trying every route. However, <a href="problem=67">Problem 67</a>, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)</p>
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