AdministratorJuly 18, 2020 at 7:15 pm
A hungry lion runs inside a circus arena which is a circle of radius 10 meters. Running in broken lines (i.e. along a piecewise linear trajectory), the lion covers 30 kilometers. Prove that the sum of all turning angles is at least 2998 radians.
Puzzle from the archives.
AdministratorJuly 18, 2020 at 7:28 pm
The solution is provided HERE. Some notes regarding the 2998 radians bound…
As pointed out by one of the comments under the problem, while 2998 radians is a lower bound for the total turning, it may not be a tight bound. If the lion travels along the circumference of the arena, his total turning will be 3000 radians. He can lower the number to 2996 + π ~ 2999.14 radians by using the following strategy:
The lion travels 20M along the diagonal, then travel 29960M along the circumference, and then travels another 20M along the diagonal.
It is an interesting question to find a better strategy (if it exists) or to improve the proof and raise the lower bound.
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