Points m, j,l and j lie on a line. Point j is between m and l , ml = 11 , kl=14 , and kj=9. What is mj?

We have points on a number lines, numbers basically, we'll call J, K, L and M.

We're interested in the lengths of line segments, which are the absolute differences of the numbers.

We have J between M and L.  Let's say L < J < M.

We have some leeway, let's just pin down L=0.  That's the origin of our number line.

Since ML=|M-L|=11 and L<M we conclude M=11.  Our inequality is

0 < J < 11.

Now we have KL=|K-L|=|K|=14 so K=14 or K=-14

|KJ|=9.

 Case 1: K=14, so 14-J=9 or 14-J=-9  so J=5 or J=23

 Case 2: K=-14 so -14-J=9 or -14-J=-9 so J=-23 or J=-5

We choose J=5 as the only one satisfying L < J < M.

L=0, J=5, M=11, K=14, MJ=|M-J|=|11-5|=6

MJ=6

Let's check ML=11, good, KL=14, good, KJ=9, good.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.