eight points lie on the circumference of a circle. one of them is labelled P. chords join some or all of the pairs of these points so that the seven points other than P lie on different numbers of chords. what is the minimum number of chords on which P lies?

If chords join "some or all" of the pairs of points, then I don't see how you can say how many chords connect to P. In principle, each point can be one end of a chord connecting to any of the seven other points.

in this case the other chords should have 7 to 1 chords.so atleast 3 chord should have P

You are correct that without any further information, it is not possible to determine the exact number of chords on which point P lies. However, we can analyze the problem and determine the minimum number of chords on which P could possibly lie.

Let's consider the worst-case scenario, where point P lies on the fewest possible number of chords. In this case, every other point on the circumference will have a chord connecting it to every other point except P. This ensures that each of the seven remaining points lies on a different number of chords.

Now, let's count the number of chords that can be formed between the seven remaining points. Since each of these points has to be connected to all other points except P, the first point can be connected to six other points, the second point to five remaining points, the third point to four remaining points, and so on.

Therefore, the total number of chords connecting the seven remaining points is:

6 + 5 + 4 + 3 + 2 + 1 = 21

Since point P is common to all of these chords, the minimum number of chords on which P lies is 21.

In summary, based on the given information, the minimum number of chords on which point P lies is 21.