I copied this question from How are the pigeonholes calculated in this pigeon-hole problem?
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 tried. But I can't understand this problem. How is it possible that there is a consecutive period of days during the runner runs exactly 17 times?
Here are my inferences:
- Runner runs daily. So each day the number of runs increases by 1 (at least)
- If he completed 15 runs in someday, the next day it will be 16, then 17 and so on.. (at least, because he runs daily)
- Then where is the period of consecutive days? I am lost here!
Mathematically it can be shown as mentioned in the linked question, but I can't understand the logic behind it. Any help would be appreciated. Thanks!