From I and II together:
Three years were in between the years in which A won a medal and the one who won a medal in long jump. A won the medal after the year 1995.
| Year | Case 1 | Case 2 | Case 3 |
| Person | Sport | Person | Sport | Person | Sport |
| 1992 | | Long jump | | | | |
| 1993 | | | | Long jump | | |
| 1994 | | | | | | Long jump |
| 1995 | | | | | | |
| 1996 | A | | | | | |
| 1997 | | | A | | | |
| 1998 | | | | | A | |
F won the medal immediately after the one who won a medal in high jump. Two persons won medals in between R and F such that R won after F.
| Year | Case 1 | Case 2 | Case 3 |
| Person | Sport | Person | Sport | Person | Sport |
| 1992 | | Long jump | | High jump/ | | High jump/ |
| 1993 | | High jump/ | F/ | Long jump | F/ | /High jump |
| 1994 | F/ | /High jump | | /High jump | /F | Long jump |
| 1995 | /F | | /F | | | |
| 1996 | A | | R/ | | R/ | |
| 1997 | R/ | | A | | /R | |
| 1998 | /R | | /R | | A | |
T did not win a medal in any of the races.
So, it can't be determined in which which year did none of the friends win any medal. So, statements I and II together are not sufficient.
From II and III together:
Three years were in between the years in which A won a medal and the one who won a medal in long jump. A won the medal after the year 1995.
| Year | Case 1 | Case 2 | Case 3 |
| Person | Sport | Person | Sport | Person | Sport |
| 1992 | | Long jump | | | | |
| 1993 | | | | Long jump | | |
| 1994 | | | | | | Long jump |
| 1995 | | | | | | |
| 1996 | A | | | | | |
| 1997 | | | A | | | |
| 1998 | | | | | A | |
L won a medal in shot put but before R. Y won a medal in the immediate year after the one who won a medal in the 100 m race. T did not win a medal in any of the races. We cannot determine the exact year of any persons among L, R, Y or T.
So, it can't be determined in which which year did none of the friends win any medal. So, statements II and III together are not sufficient.
From I and III together:
T did not win a medal in any of the races.
F won the medal immediately after the one who won a medal in high jump. Two persons won medals in between R and F such that R won after F.
| Year | Case 1 | Case 2 | Case 3 |
| Person | Sport | Person | Sport | Person | Sport |
| 1992 | | High jump | | | | |
| 1993 | F | | | High jump | | |
| 1994 | | | F | | | High jump |
| 1995 | | | | | F | |
| 1996 | R | | | | | |
| 1997 | | | R | | | |
| 1998 | | | | | R | |
L won a medal in shot put but before R. Y won a medal in the immediate year after the one who won a medal in the 100 m race.
So, it can't be determined in which year did none of the friends win any medal. So, statements I and III together are not sufficient.
From I, II and III together:
From I and II, we got:
| Year | Case 1 | Case 2 | Case 3 |
| Person | Sport | Person | Sport | Person | Sport |
| 1992 | | Long jump | | High jump/ | | High jump/ |
| 1993 | | High jump/ | F/ | Long jump | F/ | /High jump |
| 1994 | F/ | /High jump | | /High jump | /F | Long jump |
| 1995 | /F | | /F | | | |
| 1996 | A | | R/ | | R/ | |
| 1997 | R/ | | A | | /R | |
| 1998 | /R | | /R | | A | |
L won a medal in shot put but before R. Y won a medal in the immediate year after the one who won a medal in the 100 m race. One of the years should be vacant, so case 1 is invalid.
| Year | Case 2 | Case 3(i) | Case 3(ii) |
| Person | Sport | Person | Sport | Person | Sport |
| 1992 | | High jump | | 100 m | | High jump |
| 1993 | F | Long jump | Y | High jump | F | 100 m |
| 1994 | L/ | Shot put/ | F | Long jump | Y | Long jump |
| 1995 | /L | /Shot put | L/ | Shot put/ | L | Shot put |
| 1996 | R | | /L | /Shot put | R | |
| 1997 | A | 100 m | R | | | |
| 1998 | Y | | A | | A | |
T did not win a medal in any of the races. So, case 3(i) is invalid.
| Year | Case 2 | Case 3(ii) |
| Person | Sport | Person | Sport |
| 1992 | T | High jump | T | High jump |
| 1993 | F | Long jump | F | 100 m |
| 1994 | L/ | Shot put/ | Y | Long jump |
| 1995 | /L | /Shot put | L | Shot put |
| 1996 | R | | R | |
| 1997 | A | 100 m | | |
| 1998 | Y | | A | |
It cannot be determined in which year did none of the friends win any medal. So, all the three statements together are not sufficient.
Study Notes
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