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[ASK] Geometry and Series

Monoxdifly

Well-known member
Aug 6, 2015
267
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?
 

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Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,485
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.

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.
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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.
 
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