MHB What is the number below 25 in this sequence?

  • Thread starter Thread starter Monoxdifly
  • Start date Start date
  • Tags Tags
    Geometry Series
Monoxdifly
MHB
Messages
288
Reaction score
0
My partner asked me about questions no. 8 and 9.

Number 8 asks about what is the area of the quadrilateral.
Number 9 asks about what number is below the number 25.

Those are questions for Elementary School Math Olympiads in my country but both of us were having a hard time figuring them out.
For question no. 9, if only that number 9 is located right above number 13 it would be easy to solve. However, we don't know whether the placement of 9 above is intentional or not. Can someone help us solve either question?
 

Attachments

  • IMG-20200208-WA0003.jpg
    IMG-20200208-WA0003.jpg
    78.8 KB · Views: 105
Mathematics news on Phys.org
Monoxdifly said:
Number 8 asks about what is the area of the quadrilateral.
So the vertices of the quadrilateral, in particular, $C$, don't lie on the grid nodes? Then I doubt there is a nice answer.

Monoxdifly said:
Number 9 asks about what number is below the number 25.
So I can invent any rule for arranging these numbers? For example, I can place 15 to the right of 14 or I can place it in the beginning of the next line. And I can skip 0, 1, 2, etc. places after 15 or in any other place, just like 1 place is skipped after 8 for no particular reason. Then I doubt there is a nice answer.
 
For the first problem, #8, it looks like you are not expected calculate any precise values but to count rectangles, including estimating areas of partial rectangles.

For #9, I would suspect that the space between 8 and 9 shouldn't be there and write
1 2
3 4 5
6 7 8 9
10 11 12 12 14
15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31 32 33 34 35

So the number under 25 is 32.
 
Last edited by a moderator:
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...
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...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top