3 ms·
Assuming both players react instantaneously, and space is modelled as continuous (not discrete), I think the following strategy always wins for the lion. 1
by screwt 15y ago
Assuming both players react instantaneously, and space is modelled as continuous (not discrete), I think the following strategy always wins for the lion.
1. Lion runs to centre of ring
2. Lion moves toward tamer, but always staying directly between tamer and centre.
(2) is always possible, as the arc the lion has to move around to keep between tamer and centre is always shorter than any arc the tamer can move along since the lion is closer in. As a corollory, the lion can always get closer to the tamer unless the tamer moves direclty away from the centre.
Eventually the tamer reaches the edge of the ring and can no longer move directly away. Then the lion can continue to move outward, always between the tamer and centre, until they meet, and the lion eats.
- yogsototh 15y agoI believe it works only if the Lion and the tamer have a non null size (not represented as point). I am not sure of this, but if you represent the Lion and the tamer as points, the Lion can go as close as it want to the tamer, but never really reach him. Of course considering the tamer is on the border.
- gcp 15y agoNope, you're wrong.
- skyo 15y agoCan you elaborate? I was wondering the same thing as yogsototh.
- gcp 15y agoBasically there is nothing preventing the lion from reaching the tamers' coordinates exactly, i.e. it's not a case of the distance only closing "in the limit". The paper linked elsewhere here gives an illustrative example where this happens in what is clearly finite time. (This is if the tamer is on the border as parent claimed - the paper also shows that the lion can't win if he doesn't do this)