A trail, two days and a conclusion that seems impossible to guarantee until you find the right angle to look at it.
The monk and the mountain
Riddle statement
A monk climbs a mountain along a narrow path. It leaves at dawn and reaches the summit at dusk. Spend the night there.
The next day go down the same path. He also leaves at dawn and arrives at the foot at dusk.
He may have walked at different speeds in different sections, stopping at different places and resting at different times on each day.
Can you be sure that there is at least one point on the path that the monk passes through at exactly the same time on both days?
Show solution
Solution
Imagine two different monks:
one does the uphill route on the first day;
the other does the downhill route on the second.
Suppose that they both walk the path on the same day: one starts from the foot of the mountain and the other from the top, both at dawn.
As they advance along the same path in opposite directions during the same time interval, they must There will come a time when they intersect.
That moment and that place are exactly what we were looking for: a point on the path that the first monk passed at a certain time and that the second passed at that same time—that is, a point that the real monk traveled at the same time on both days.
Therefore, yes: that point always exists, regardless of the rhythm or the breaks of each day.