Which among the following statement(s) is/are not true?

I. M plays cricket
II. No one plays after O
III. P plays before the one who plays tennis

Study the following information carefully and answer the given questions below:

Six persons plays different sports on six different days from Monday to Saturday of a week. The sports are- Football, Cricket, Basketball, Tennis, Golf and Squash (but not played in the same order as given).

Only two persons play between the one who plays football and O. Not more than two persons play after O. As many persons play before the one who plays football as after the one who plays basketball. P plays just after M but three persons before the one who plays basketball. The one who plays squash plays three persons before R but after M. Q doesn’t paly squash and plays after the one who plays cricket. N doesn’t play football. The one who plays golf play before R.

The correct option is Only II.

Step-by-Step Explanation:

Let us arrange the six persons and their respective sports across six days of the week, from Monday to Saturday, by logical deduction based on the given clues:

1. Days of the week: Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5), Saturday (6).

2. Positions of P, M, and Basketball:
It is given that "P plays just after M but three persons before the one who plays basketball."
This means the order is M, followed immediately by P, and then two persons between P and the Basketball player.
So, if M is at position x, P is at x+1, and Basketball is played at x+1+3 = x+4.
Since Basketball must be within 6 days (1 to 6), x+4 ≤ 6, which gives x ≤ 2.
- If M = Monday (1), P = Tuesday (2), Basketball = Friday (5).
- If M = Tuesday (2), P = Wednesday (3), Basketball = Saturday (6).

3. Positions of Football and Basketball:
Clue: "As many persons play before the one who plays football as after the one who plays basketball."
- Case 1: If Basketball is on Friday (5, i.e., 1 person plays after Basketball), Football must be on Tuesday (2, i.e., 1 person plays before Football). But P plays on Tuesday in this case, and P plays 3 persons before Basketball. Let's check Football and O: "Only two persons play between Football and O." If Football is Tuesday (2), O would be Friday (5). But Basketball is on Friday (5). Thus O plays Basketball.
Also check: "Not more than two persons play after O." If O is Friday (5), 1 person plays after O, which satisfies the condition.
- Case 2: If Basketball is on Saturday (6, 0 after), Football is on Monday (1, 0 before). Then O would be Thursday (4) since 2 persons play between Football and O. Then 2 persons play after O, which also satisfies "not more than two persons play after O". But let's check Squash: "The one who plays squash plays three persons before R but after M." That means Squash is 3 positions before R (Squash at y, R at y+3). In Case 2 (M on Tuesday), Squash must be after M, so Squash can be Wednesday (3) -> R is Saturday (6). But R would play Basketball, and Squash is Wednesday. Let's test both cases thoroughly.

Let's verify Case 1:
- Monday (1): M
- Tuesday (2): P (plays Football)
- Wednesday (3): Squash player (since Squash is after M, and 3 persons before R: 3+3=6, so R is Saturday)
- Thursday (4): Golf player (since "The one who plays golf plays before R")
- Friday (5): O (plays Basketball)
- Saturday (6): R

Now place remaining people (Q and N):
- "N doesn't play football." Since Football is on Tuesday (P plays Football), this is fine.
- "Q doesn't play squash and plays after the one who plays cricket."
The available days for Q and N are Wednesday (3) and Saturday (6) or Thursday (4). But R is on Saturday (6).
So the remaining persons are Q and N for Wednesday (3) and Thursday (4).
Since Q doesn't play Squash (Wednesday), Q must be Thursday (4), and N must be Wednesday (3).
Thus:
- Monday (1): M (plays Cricket)
- Tuesday (2): P (plays Football)
- Wednesday (3): N (plays Squash)
- Thursday (4): Q (plays Golf)
- Friday (5): O (plays Basketball)
- Saturday (6): R (plays Tennis)

Let's check all constraints against this final arrangement:
- Monday: M (Cricket)
- Tuesday: P (Football)
- Wednesday: N (Squash)
- Thursday: Q (Golf)
- Friday: O (Basketball)
- Saturday: R (Tennis)

1. Football and O: Football (Tuesday, 2) and O (Friday, 5) -> 2 persons (Wednesday, Thursday) between them. (Satisfied)
2. Not more than 2 persons after O: O is Friday, only 1 person (Saturday) after O. (Satisfied)
3. Persons before Football = Persons after Basketball: 1 before Football (Monday), 1 after Basketball (Saturday). (Satisfied)
4. P plays just after M: M (Monday), P (Tuesday). (Satisfied)
5. P plays 3 persons before Basketball: Tuesday + 3 = Friday (Basketball). (Satisfied)
6. Squash plays 3 persons before R: Squash (Wednesday, 3) + 3 = Saturday (R). (Satisfied)
7. Squash after M: Wednesday is after Monday. (Satisfied)
8. Q doesn't play squash and plays after cricket: Q is Thursday (Golf), Cricket is Monday. (Satisfied)
9. N doesn't play football: N is Wednesday (Squash). (Satisfied)
10. Golf before R: Golf is Thursday, R is Saturday. (Satisfied)

Now let's evaluate the given statements to find which is/are NOT true:

Statement I: M plays cricket -> TRUE (M plays cricket on Monday).
Statement II: No one plays after O -> NOT TRUE (R plays after O on Saturday).
Statement III: P plays before the one who plays tennis -> TRUE (P plays on Tuesday, Tennis is played on Saturday).

Therefore, the statement which is NOT true is Only II.