Monday, July 20, 2009

Fox 94




Observe how the rod moves inside the prism.
What can be the maximum length?

22 comments:

  1. No, it should not be.
    The prism is hollow. The rod goes in from the top, turns the corner inside the prism and leaves from the bottom right.
    The rod linear and not bending.
    Also assume that top and right-hand side prisms (small one) are long enough - as seen.

    This is a hard geometry problem. Solving Fox 93 gives you an idea on this solution. 93 should be posted here:
    http://www.8foxes.com/Home/93

    Good luck.

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  2. But i still didn't understand, rod can touch the bottom at infinity while it touch the corner

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  3. No, the connected prism is an L-shaped tube. The only enterance is from the TOP, and it leaves from the RIGHT-HAND-SIDE. It's walls are rigid.

    As you say the rod can go to infinity while touching the corner, BUT, it can not come to that position by entering from the TOP.

    Have you ever carried a long piece of wood or pipe around an L-shaped corridor?

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  4. but think about a infinit length rod entering from the top

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  5. And how is it gonna turn around the corner???

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  6. my english is not good
    maybe i am missing something

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  7. by meaning go around do you mean entering from top and leaving from bottom?

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  8. Entering from Top, leaving from Bottom-Right.

    The answer is the same if it enters from Bottom-right and leaves from the Top.

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  9. i think the answer is C
    but i guess it is B
    http://i38.tinypic.com/2py59ts.gif

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  10. newzad,
    Your answer is posted above. You're on right path. But the answers to both foxes (93 and 94) are exact! Not an approximation. There may be a minor mistake in your approach. We have a different answer. We would insists on solving Fox 93 first:
    http://www.8foxes.com/Home/93

    Then you can add another dimension and try solving Fox 94.
    Thanks.

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  11. For Fox 93:

    sin(2alpha)=1/a
    cos(2alpha)=8/b
    Length of the rod = L = a+b = f(alpha)

    Minimum value of f(alpha) gives the maximum length of the rod (why?)

    Fox 94 may have a different solution.

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  12. This comment has been removed by the author.

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  13. I remember seeing a solution here. what happened?

    sin(2alpha)=1/a
    cos(2alpha)=8/b
    Length of the rod = L = a+b = f(alpha)
    gIVEN by O. alpha=q
    L=1/sin(2q) + 8/cos(2q)
    L'=-(cos(2q)*2)/sin^2(2q) + sin(2q)*2*8/cos^2(2q) = 0 the min value of L can go tru the corner.
    i am skipping 2nd order condition (L''>0)

    2cos^3(2q)=16sin^3(2q) gives the answer.

    binary descartes

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  14. Hey binary:
    That's the solution for Fox 93. Not this one.
    Fox 94 can be solved with the same logic, but a little more work is needed, We'll post Fox 93 here as well.

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  15. newzad: the rod must touch the following points at the same time:
    1. upper-left corner at the back AND
    2. common line segment between upper prism and lower prism AND
    3. lower-right corner in the front

    intuitively thats what i see.
    -binary descartes

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  16. yes,
    and how will you solve?
    can you show your solution?

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  17. I have to go for now tomorrow i have an exam
    i will be here for a few hours later
    post your answer

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  18. i don't have the solution yet. no time to solve actually.something similar to ur good solution to 93 would work. do this:
    drop a normal line from common segment line (point 2 in my previous post) also draw the projection of the rod on the base.there should be pithagoras and congruent right triangles. then right the length of the rod in terms of one of the lengths (or an angle). then we may get a function to differantiate. will try myself here. but later.
    -binary descartes

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  19. İ think i have to say again
    for this problem you have to add 16
    fox 93 the answer was 5sqrt(5)=sqrt(125)

    for this question there is a more dimension different from fox 93

    and this dimension doesn't effect the rod while going through the corner

    so for the biggest length this dimension must be 16

    a^2+b^2+c^2 must be the biggest

    a^2+b^2=125 which proved at fox 93
    c^2=16

    ROD=sqrt(125+16)=sqrt(141)

    it is solution is similar to fox 93

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