MathDB

Let

A,B

denote two distinct fixed points in space. Let

X, P

denote variable points (in space), while

K,N, n

denote positive integers. Call

(X,K,N,P)

admissible if (N \minus{} K) \cdot PA \plus{} K \cdot PB \geq N \cdot PX. Call

(X,K,N)

admissible if

(X,K,N,P)

is admissible for all choices of

P.

Call

(X,N)

admissible if

(X,K,N)

is admissible for some choice of

K

in the interval

0 < K < N.

Finally, call

X

admissible if

(X,N)

is admissible for some choice of

N, (N > 1).

Determine: (a) the set of admissible

X;

(b) the set of

X

for which

(X, 1989)

is admissible but not

(X, n), n < 1989.

Problem Statement