Game of Cat and Mouse - Numberphile
Numberphile・20 minutes read
The puzzle involves a cat chasing a mouse in a pond, with different tactics explored for the mouse to escape successfully, including circling to maintain a specific distance from the cat. Using a specific scale factor and distance from the center, the mouse can outpace the cat and reach a "sweet spot" for successful escape, highlighting the complexity and intrigue of the scenario.
Insights
- The cat and mouse puzzle involves various tactics for the mouse to escape the cat, including swimming towards the farthest point, dashing to the edge, and circling at a specific distance to outpace the cat.
- The success of the circling tactic in evading the cat depends on maintaining a specific distance from the cat, with a scale factor of one quarter and utilizing the concept of event horizons to create a "mouse sweet spot" for successful escape.
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Recent questions
How does the mouse attempt to escape the cat?
By swimming away but failing to evade interception.
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Summary
00:00
Cat and Mouse Pond Escape Strategies
- The puzzle involves a cat chasing a mouse in a pond, with the mouse being faster than the cat but inadvertently entering the water.
- The cat is depicted to scale, with added ears, sitting on the edge of the pond, waiting for the mouse to leave.
- The mouse, although faster on land, is assumed to slow down in water but can swim without drowning.
- The cat is established to be four times quicker than the mouse in terms of walking or running versus swimming.
- The mouse attempts to escape by swimming away from the cat, but this tactic proves unsuccessful as the cat can always intercept.
- Another tactic suggested is for the mouse to swim towards the point farthest from the cat, but this also fails as the cat can still catch up.
- Two additional tactics are introduced: the dash tactic, where the mouse swims towards the nearest edge, and the circling tactic, where the mouse moves in circles to try and evade the cat.
- The dash tactic is unsuccessful if the mouse starts from the center of the pond, as it cannot reach the edge before the cat intercepts.
- The circling tactic's success depends on the distance between the mouse and the cat, with a specific distance acting as a critical point for escape.
- The circling tactic involves the mouse trying to match the cat's speed by circling in a smaller radius, with success hinging on maintaining a specific distance from the cat.
11:49
"Cat and Mouse Escape Tactics with Pi"
- A scale factor of one quarter is used in the scenario, with the distance from the center being one quarter.
- The circle allows the mouse to outpace the cat in terms of angles, with a specific distance of 0.25 meters from the center.
- Two event horizons are established, with a dash boundary and a circling boundary, creating a "mouse sweet spot" for escape.
- Using GeoGebra, a tactic is implemented for the mouse to reach the sweet spot, circle until opposite the cat, and then escape successfully.
- The mouse's speed compared to the cat's speed is crucial, with a ratio of 4 allowing for successful escape, while adjustments in speed ratios affect the size of the sweet spot.
- The puzzle involving the cat and mouse, along with the significance of the number pi in determining escape possibilities, is highlighted, showcasing the complexity and intrigue of the scenario.
