South Asian Finals!
Five nations competed in the finals of the South Asian Track Meet. They were
China
,
India
,
Singapore
,
Thailand
, and
Vietnam
. The five events in the finals were: the high jump, shot put, 100 meter dash, pole vault and 4 by 100 relay. In each event the nation placing first received five points; the one placing second, four points; the one placing third, three points; and so on. Thus, the one placing last received one point. At the end of the competition, the points of each nation were totaled, and the totals determined the final ranking.
-
(a) - China won with a total of 24 points.
-
(b) - "Troy Nguyen" of Vietnam won the high jump, while "Steve Tran", also of Vietnam , came in third in the pole vault.
-
(c) - Singapore had the same number of points in at least four of the five events.
Each nation had exactly one entry in each event. Assuming there were no ties and the nations ended up being ranked in the same order as the alphabetical order of their names, in what position did "Satyajit Mohanty" of India rank in the high jump?
Image Credit: Telegraph (UK)
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Since each nation had exactly one entry in each event, we conclude by (a) that China had four first place finishes and one second place finish. By (b) it becomes clear that the one second place finish they had was in the high jump. Thus "Satyajit Mohanty" of India could finish no higher than third place in the high jump. Of the total of 75 available points, 24 went to China, which leaves 51 points to be shared by the other four nations. Since they all received different totals, India, who came in second must have obtained at least 15 points (since 14+13+12+11 = 50, which is too small).
A similar argument shows that last place Vietnam must have obtained at most 11 points (since 12 + 13 + 14 + 15 = 54, which is too large). Since Vietnam obtained 5 points for the high jump and 3 points for the pole vault by (b), and at least 1 point for each of the other three events, they must have a total of at least 11. This, together with our previous remark shows that Vietnam had exactly 11 points. This leaves only 40 points to be shared by India, Singapore, and Thailand, and each of them must have at least 12 points. The only possibility is that India had 15 points, Singapore had 13 points and Thailand had 12 points. Since Singapore received the same number of points in four of the five events and had a total of 13 points, they must have finished third four times and last once (since four second place finishes would give them too many points, while four fourth place finishes would require them to finish first in the other event to get 13 points, but all the first place finishes went to China and Vietnam).
Thus Singapore had to finish last in the pole vault, as Vietnam finished third. At this point we have determined that all 1-point, 3-point, and 5-point finishes (except for last place in the high jump) have gone to one of China, Singapore, or Vietnam. Since the only remaining odd point will generate an odd total, it must go to India, which has a total of 15 points. Thus "Satyajit Mohanty" of India must have finished last (fifth) in the high jump.