Maths Question for fun?

Question

Let n ≥ 2 be a positive integer. Initially, there are n fleas on a horizontal line, not all at the same point.

For a positive real number λ, define a move as follows:

Choose any two fleas at points A and B, with A to the left of B;

let the flea at A jump to the point C on the line to the rightof B with BC/AB=λ.

Determine all values of λ such that point M on the line and any initial positions of the n fleas, there is a finite sequence of moves that will take all the fleas to positions to the right of M

Answer 1

If you need homework help, just ask.

Answer 2

Math is never fun on Winter break.