Five young athletes named Jay, Ken, Lee, Mike, and Nick took part in
a contest of five events: the high jump, the shot put, the mile run, the
hurdles, and the 100-meter dash. It was agreed that a first-place finish
would receive 1 point, a second-place finish 2 points, and so on;
and that the competitor with the lowest point total would be declared
the overall pentathlon winner. As it turned out, there were no ties in
any single event, and no ties for overall points in the pentathlon.
When the meet was over, the five athletes made a number of statements,
which are recorded below. These statements, all true, will enable a
dedicated logician to determine the placement of all the
athletes in each event and in the final standings.
STATEMENTS
JAY:
1. Mike beat me in the high jump,
but lost to Lee in the shot put.
2. Ken finished with 14 points in the
pentathlon.
KEN:
3. Mike was first in two events, but
he did not win the pentathlon.
4. Jay did not finish last in the mile or
the shot put, but Nick was last in the
hurdles.
LEE:
5. Nick beat me in the shot put and
in just one other event, and he beat
Jay in the high jump; but Nick did not
place first in either the shot put or
high jump.
6. Jay finis~ed one place ahead of
me in the hurdles, but lost to me in
the shot put.
MIKE:
7. Ken beat Nick in the mile, but lost
to him in the 1 OO-meter dash; neither
man placed first in either event.
8. I did not win the mile, and Jay did
not finish second in the 100-meter
dash.
NICK:
9. Jay finished in a different position
in each event.
10. Without winning either event, Lee
beat Mike in the high jump, and beat
Ken in the mile.
High Jump Shot Put Mile
1. 1. 1.
2. 2. 2.
3. 3. 3.
4. 4. 4.
5. 5. 5.
Hurdles Dash
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.