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I am trying a variation of snails moving in an equilateral triangle.

Suppose that you have $6$ snails arranged on the the surface of a sphere such that they are equidistant from each other. All the snails are numbered from $1$ to $4$. The snail numbered $1$ moves toward snail numbered $2$, and $2$ moves towards $3$, $3$ moves towards $4$, $4$ moves towards $5$, $5$ moves towards $6$, $6$ moves towards $1$,

If they move at a certain speed $v$ when and where would all the snails meet.

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closed as off-topic by BMS, Kyle Kanos, JamalS, DavePhD, jinawee May 18 '14 at 16:05

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It would depend on the numbering of the snails and the direction they start out in. If you number the snails like a die, and snails 1 and 4 move in a certain direction at start, you end up with 2 groups of 3 on opposite sides of the sphere. – LDC3 May 18 '14 at 14:43
This is probably better suited to math.SE than physics, but also you will need to give more details about the geometry. Six snails all equidistant from each other is impossible AFAICT (I don't think you can have more than 4), and in general the order of the numbers will matter as well, as LDC3 said. – Nathaniel May 18 '14 at 14:45
actually this a physics problem, you can find similar problem presented, you project the motion of the objects to find where they meet, and i have edited the problem. – Derg May 18 '14 at 14:59
@LDC3 The direction is defined right? It is in the direction of the chased snail. – Bernhard May 18 '14 at 15:09
If the snails can move freely through space, the answer is at If they must stay on a sphere of constant radius, I would think they never meet. They would form a rotating tetrahedron. – mmesser314 May 18 '14 at 15:10