The worlds first riddle!

"V = X / II * L * XX "


Perhaps a horizontal bar over or under the V means 5000?
I tried everything, well surely not everything, but can't find this 'easy' one.
Am I blind? It's a real good puzzle.


"IV - X = VI - I"


The only positive thing what came from my trying your sneaky one, is that I though of another one for you to try.


I - VII = X - VI


Whim

1. 5 marks
How many non-congruent strictly isosceles triangles can be constructed using only 3 cm, 7 cm or 10 cm lengths for the edges?

0

Edit: Forget this I thought all three edges were on one triangle.

Four: 10-10-3, 10-10-7, 7-7-10, 7-7-3.


whim

"Perhaps a horizontal bar over or under the V means 5000?" A horizontal bar over a letter multiplies its value by 1000.

I - VII = X - VI

I -V I - I = X - VI
abs(-5) - 1 = 10 - 6

Nope, that not the solution I had in mind. I do not understand how your equation works. The way I see it you say: -6 = 4

The first and second Is (surrounding the -V) are the symbols for absolute value (two vertical bars surrounding an expression). The absolute value is always non-negative.

"IV - X = VI - I"

I give up Mark.

Whim:
IV - X = VI - I

I used absolute value here.

| V-X | = VI - I

MRC 2004 (part 1)

I'd like to file an official protest concerning the ambiguity of problem 4.
I see the configuration that leads to this answer. However, there are many other configurations where the circles are tangent to each other and the rectangle at at least one point.

MRC 2004 (part 2)

6. 12/5 or 2.4

7. 6912/625 (assuming this is related to problem 6)

8. 5/16 if leading zeros allowed (otherwise 1/4)

9. 85

10. 301

Mark wrote, "I'd like to file an official protest concerning the ambiguity of problem 4.
I see the configuration that leads to this answer. However, there are many other configurations where the circles are tangent to each other and the rectangle at least one point."

The international appeals committee sitting in secret session issued the following announcement.

For immediate circulation:

The protest has been upheld

I'd like to thank the international appeals committee. I won't hold my breath waiting for the publishing of the reasons.

I will pass your comments to the IAC. :wink:

Amazing, simply amazing.

6. 2.4 cm
7. 35
8. 5/16
9. 85
10. 301


MRC 2004 (part 3)


11. 10 marks
Three persons A, B and C are situated on the same vertex of a regular polygon. They all start walking at the same time around the boundary of the polygon. A walks in the opposite direction to B and C.
A meets B on a certain vertex. Two vertices later A meets C.
A's speed is twice that of B and B's speed is twice that of C.

How many vertices does the polygon have?


12. 10 marks
How many triangles can be constructed so that the length of its sides are three consecutive odd integers, and its perimeter is less than 1000?


13. 10 marks
A box contains 900 cards, each having a different integer from 100 to 999 inclusive written on it. You draw cards at random from the box and compute the sum of the digits of the number on it.
How many cards do you have to draw to be sure that at least three of those cards give the same digit sum?


14. 10 marks
Consider the function f(x)=cx/(2x+3). Find all values of c for which f(f(x))=x.


15. 10 marks
A vertical line intersects the parabola in the point A and intersects the line x-y=2 in the point B. Find the minimum distance between the points A and B.

Do you have an explanation for 7? Were words left out of the problem statement?

MRC 2004 (part 3)
11. 15

12. 164

13. 53

14. -3

15. 0? (This appears to be the ambiguous problem in this set.)

Mark wrote, "Do you have an explanation for 7? Were words left out of the problem statement"

From what I recall, a line is missing. I am sure the full question did not relate to the previous one. However, your answer did bridge the gap.
In my poor defence, I must say that my practice of cut and paste will be replaced with copy and paste so I will be able to check the original.
It is fair to say both questions and answers have been reduced to the minimum, if this causes problems, give a best guess or a miss.

11. 15
12. 165
13. 53
14. -3
15. 3/2


MRC 2004 (part 4)(Last)

Replacement Q4.

I- 8 + 8 + 8 = I + 8 + HI

Clue: Remove a segment.
Hint: Look for the answer at a different angle.



16. 10 marks
Let where [x] is the greatest integer less than or equal to x. Determine the number of isolated points of the graph of f.


17. 20 marks
Two circles with radius 1 touch each other at the point G. Their common diameter intersects one circle also in the point A. The points B and C are each on a different circle. The line BC contains G and meets the common diameter at an angle of 45 degrees. Determine the area of triangle ABC.


18. 30 marks
How many distinct values can be obtained by mulitplying two distinct numbers from the set {4,8,9,16,27,32,64,81,243}?


19. 45 marks
Two numbers are such that the sum of their cubes is 5 and the sum of their squares is 3. Find the sum of the numbers, given that the sum is rational.


20. 45 marks
The diagonals of a square ABCD meet at E and the bisector of intersects DE in G and DC in F. If GE=sqrt(5), determine FC.

End (Fin) (Ende)

If there's 1 part of math I have always liked it's geometry.

Try, I believe the length of your football club is @[]%.

Surely this is not the fin.