The question is as follows:
To prepare for a marathon, an elite runner runs at least once a day over the next 44 days, for a total of 70 runs in all. Show that there's a period of consecutive days during which the runner runs exactly 17 times.
I know the mechanics of solving it. It is:
Let $r_i$ be the total number of runs as of day $i$.
$1 \le r_1 \le r_2 \le r_3 \ldots \le r_44 = 70$
Let's do $r_i + 17$
$18 \le r_1 + 17 \le r_2 + 17 \le \ldots \le r_44 + 17 = 70 + 17 = 87$
Now counting the pigeons:
$r_i$ is $44$ values
$r_i + 17$ is $44$ values. $44 + 44 = 88$ pigeons.
The pigeonholes are the $87$ values available. So by the pigeonhole principle
$r_i = r_j + 17 \le i > j$ (I don't really get this part).
My main issue is how are the pigeons calculated to be $44 + 44.$