How many 14ers did I climb?
C, 174 bytes
a[99],c,p,j,M,m;main(i){for(i=j=1;c=getchar(),~c;i++)c&lt;11?a[i]=j++,i=0:c&amp;4?a[i]=j:0;for(m=j;c=a[i++];c&gt;a[i-2]?M-m&gt;1&amp;&amp;c-m&gt;1?M=c,m=j,p++:M&lt;c?M=m=c:M:m&gt;c?m=c:0);printf(&quot;%d&quot;,p);}

Requires a trailing newline in the input, otherwise +4 bytes.