In a cycling competition with $14$ stages, one each day, and $100$ participants, a competitor was characterized by finishing $93^{\text{rd}}$ each day.What is the best place he could have finished in the overall standings? (Overall standings take into account the total cycling time over all stages.)
Problem
Source: Puerto Rico TST 2014
Tags: combinatorics
Konigsberg
29.04.2015 09:05
lol this is a mathcounts-level problem. Best is 16th place. very easy
fprosk
01.05.2015 07:22
That's not the answer...
Konigsberg
01.05.2015 19:42
Darn its second place SHOOT
fprosk
01.05.2015 19:44
Haha yep
Konigsberg
02.05.2015 19:08
is this really an IMO TST?
MATH1945
31.05.2015 12:54
93 - 7 x 13 = 2
anubhav11
31.05.2015 22:26
The problem would have been slightly better if the final rankings were the cumulative of the rankings in the 14 events.
TheWalkingD
27.06.2016 06:08
Generic_name wrote: MATH1945 wrote: 93 - 7 x 13 = 2 Hello can you please explain this. The total cycling time is taken into account, so you can ruin your whole result by taking really long once. Suppose everyone slower than the 93rd would be infinitely bad, its easy to see that, in the best case, this fate hits 7 different people over all 14 stages, so the total amount of partitipants "elimimated" this way is $14 \cdot 7=98$, for which he Could be second.