Velocity of any ant U =(11−k)2−k2=121−22k Now at any time distance travelled by any ant will be S=S0+ut Where S0 is the initial position Now two ants will be at same position If Si=Sj ki2−22kit+121t=kj2−22kjt+121t t=
kj2−ki2
22(kj−ki)
⇒t=
kj+ki
22
Now for i = 1 Values of t will be
3
22
,
4
22
,
5
22
,....
.11
22
(9 values) for i = 2 values of t will be
4
22
,
5
22
,....,
11
22
,
12
22
We can see there is only 1 distinct value Similarly of i = 3,4,5,6,7,8,9 we get only 1 distinct value each. So in all there 17 distinct values of 't'