The First Female Drafted Into The NBA
In 1969, Denise Long became the
first female to be drafted into the NBA
. In the previous year, she led the Union-Whitten High School basketball team to the state title, averaging an impressive 62.8 points per game. The most points that she scored in a game that season was an astonishing 111. (This feat was only done once.)
Given that there are 30 games in the season of 1968, what is the smallest possible number of points that she could have scored in her second best game?
Note: She scored a non-negative integer number of points in each game.
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.
3 solutions
i too thought it must be 61 as it is much closer to it than 62
Log in to reply
With the pigeonhole principle (which is essentially the argument above) you have to take the ceiling function.
Otherwise, if she only scored a max of 61 for 29 games, then her maximum score is 6 1 × 2 9 + 1 1 1 = 1 8 8 0 , which contradicts that she scored 1884 for 30 games.
oh i thought it close to 61
I think the answer must be 9. Reading the problem, I think it is possible to score 111 points not only once. She scored 1884 points in total. Dividing 1884 by 111, giving 16. 97 rounded to the nearest hundredths. Meaning, it is possible that she scored 111 points each in 16 games. 1884 - (111x16) = 108. It means that it is possible that she scored 108 points for 14 games. So it is possible also that she scored 9 points each in 12 games and nothing in the remaining 2 games. So, I bet 9 is the correct answer.
Log in to reply
Log in to reply
Sorry, I do not understand what you're trying to say.
She scored 111 only once in 1 game. I do not understand why you took 1884/11. I do not understand anything else after that.
Log in to reply
@Calvin Lin – I figured it out! Jayver interpreted "second best game" as "second highest distinct score achieved". That's clearly an incorrect interpretation, but the problem he solved is actually kind of even more interesting than the original. :-) Unfortunately Jayver, there's still a small error in your solution!
Log in to reply
@Kevin Bourrillion – Hello. Please help me. I got confused because I think it is obviously true that second best game is the second highest distinct score achieved. For example, it is stated that 111 points is her highest score achieved during that season. So it is considered that a game where she scored 110 points is her 2nd best game. And from the statement "The most points that she scored in a game that season was an astonishing 111", it is possible that it happened not only once. I think that part of problem brought my confusion. Thanks a lot. More power to Brilliant. :)
Log in to reply
@Jayver de Torres – If she score 111 points several times, then her "second best game" would be a score of 111 points. I've added "(This feat was only done once.)" to reduce the confusion.
However, even with your interpretation, 9 isn't the correct answer. She can score 111 in 16 games, and then 8 for 13 games and 4 in 1 game, which would make the "second highest distinct score" 8. It remains to show that this is the smallest possible.
@Jayver de Torres – @Calvin Lin
@Kevin Bourrillion – Ah, that makes some sense. Thanks!
It asked for "the second best game", so I think is clear enough. Let me try and edit it for more clarity.
Little late I know, but even 9 isn't the minimum. With that line of reasoning, we can choose 13 games with 8 points each and one game with 4 points. So 8 would be the second highest one
According to me the statement "The most points that she scored in a game that season was an astonishing 111" specifies it occurred in 1 game
After dividing the 1884-111=1773 into 29 equal parts (considering as a line segment of length 1773 units)using 30 vertical sticks if you try to make any of the part more smaller the other gets increased so it cannot be less than 1773/29 and the next greater integer is 62.
In total she scored 6 2 . 8 × 3 0 = 1 8 8 4 points.
That means in the other 29 games she scored 1 8 8 4 − 1 1 1 = 1 7 7 3 points, averaging 2 9 1 7 7 3 ≈ 6 1 . 1 4 points per game.
Obviously, her best game (of the other 29) is above average, so 6 2 points.
Example : 25 games with 61 points, 4 games with 62 points, 1 game with 111 points
After dividing the 1884-111=1773 into 29 equal parts (considering as a line segment of length 1773 units)using 30 vertical sticks if you try to make any of the part more smaller the other gets increased so it cannot be less than 1773/29 and the next greater integer is 62.
First, mentioned that she played 30 matches with the average points of 62.8.
So, in that season, she scored 6 2 . 8 × 3 0 = 1 8 8 4 points in total
Now, except from her best scoring game: 111 points, she scored 1 8 8 4 − 1 1 1 = 1 7 7 3 points in total in other 29 games
So, in these 29 games, the average points which she had scored are 2 9 1 7 7 3 ≈ 6 1 . 1 4
So the least points she had to score in her second best game is the smallest integer which is larger than 61.14. This number is 62
And this is the answer to solve this problem!