A seventh grade and eighth grade student problem

  • Thread starter Thread starter K Sengupta
  • Start date Start date
  • Tags Tags
    Student
AI Thread Summary
In a tournament involving seventh and eighth graders, each contestant played against every other contestant once. There were significantly more eighth graders, with a ratio of ten to one compared to seventh graders. Despite this, eighth graders only managed to win four-and-a-half times the points of the seventh graders. The problem concludes that there were 2 seventh graders who achieved 4 wins, while 20 eighth graders won a total of 18 matches. This illustrates a competitive dynamic where fewer seventh graders performed effectively against a larger group.
K Sengupta
Messages
113
Reaction score
0
Seventh- and eighth-grade students participated in a tournament. Each contestant played each other contestant once. There were ten times as many eighth-grade students, but they were able to win only four-and-a-half times as many points as seventh graders.

How many seventh-grade students participated, and how many points did they collect?

Note: Assume one point for every win, and no drawn outcomes.
 
Mathematics news on Phys.org
Spoiler:There were 2 seventh graders who had 4 wins and 20 eighth graders who had 18 wins.
 
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top