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Oct 26th, 2021, 2:16am

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 1   riddles / easy / Re: How many cats are in the box?  Oct 7th, 2021, 7:16am 
Started by Arne | Last post by jollytall
It all depends on the weight (mass) of the box. I would say it is fair to assume that a box capable of holding 7 cats is at least as heavy as 2 cats...
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 2   riddles / easy / Re: Number of triangles  Aug 27th, 2021, 9:05am 
Started by navdeep1771 | Last post by rmsgrey
Do you count the degenerate traingle with sides 1004/502/502?
 
If so, then I make it 87
 
Reasoning:
hidden:
a right isosceles triangle has sides in ratio 21/2:1:1 and 2008/(2+21/2) is just over 588. Since any integer length for the matching sides will give an integer length for the remaining side, any integer from 502 to 588 will give an isosceles triangle with angle greater than a right angle.
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 3   riddles / medium / Re: Maximum Separation  Aug 13th, 2021, 7:29am 
Started by navdeep1771 | Last post by rmsgrey
Answer: Lmax=(v1+v2)2/(2(a1+a[s ub]2[/sub]))
 
Working:
::
hidden:

Working in a frame where one of the bodies is stationary throughout (and ignoring relativistic corrections), the other body has initial velocity, u=v1+v2, and constant acceleration in the opposite direction, a=a1+a2.
 
The change in separation between the two bodies, s, at a given time, t, is given by standard SUVAT formulae:
s=ut-at2/2
Since s reaches a maximum when the closing velocity, v=u-at, is 0, we get:
u-at=0
t=u/a
Substituting for t in the equation for s gives:
s=u(u/a) - a(u/a)2/2
=u2/a - u2/2a
=u2/2a
and substituting back for u and a gives the answer above:
Lmax=(v1+v2)2/(2(a1+a[s ub]2[/sub]))
::
 
edit: the subscript tags are behaving weirdly, and I can't get them to work properly
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 4   riddles / medium / Re: Covering square with 2x1 rectangles  Aug 11th, 2021, 12:54pm 
Started by rmsgrey | Last post by Grimbal
1 rectangle: obvious.
 
I.e. the square must be covered by one rectangle.  That rectangle must have area 1 and ratio 2:1.  The rectangle must have dimensions sqrt(2) by sqrt(0.5).  The diagonal of the rectangle is sqrt(2+0.5) = sqrt(2.5).  This diagonal doesn't fit in the square with diagonal sqrt(2).  So a rectangle with sufficient area doesn't fit in the square.
 
(Or more simpler: the square isn't a 2:1 rectangle.)
 
3 rectangles:
There are 4 corners and only 3 rectangles.  One rectangle must fill two corners.  That rectangle must have size is 1 x 0.5.  The remaining area is also a 1 x 0.5 rectangle.  And  it must be filled by wo rectangles. Again, one rectangle must fill 2 corners of that area.  This leaves only 2 ways, 1 x 0.5 or 0.5 x 0.25.  One way doesn't give space for a third rectangle, the other leaves a 3:2 space which is not the right ratio.
 
4 rectangles:
If one rectangle fills 2 corners, there is always one rectangle that must fill a whole side.  That leaves few possibilities.
The first rectangle would be 1 x 1/2.  The second can only be 1/2 x 1/4.  The third can be 1/2 x 1/4 leaving a 1/2 x 1/2 space or 3/4 x 3/8 leaving a narrow 3/4 x 1/8 rectangle.  Both are the wrong ratio.
 
So remains the case where each corner of the square is filled by a different rectangle.
 
In that case, consider a rectangle that touches the center of the square.  There must be one.  That rectangle must reach from a corner to the center.  It must have at least 1/2 in both dimensions, which actually means it must have dimensions 1 x 1/2.  We are back to the previous case which didn't work.  (Or in fact we contradict the hypothesis that each corner is filled by a different rectangle).
 
I think that covers it.  No pun intended.
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 5   riddles / what am i / Re: Card Magician: A Trick  Jun 27th, 2021, 6:02am 
Started by alien2 | Last post by alien2
SPOILER: All cards were the same.
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 6   riddles / easy / Re: Rubik's Cube  May 10th, 2021, 4:53am 
Started by alien2 | Last post by Grimbal
I see.  I doughnut-shaped cube.
 
And yes, to some people that makes perfectly sense.
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 7   riddles / easy / Re: Assemble 100  Apr 29th, 2021, 12:06am 
Started by Moti | Last post by Grimbal
9+9+9+9 = 36 = 1006
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 8   riddles / what am i / Re: Nickel, anyone?  Apr 8th, 2021, 10:11am 
Started by alien2 | Last post by alien2
Yes. And no regarding something other than a nickel. It's the same hand in "both" cases.
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 9   riddles / what am i / Re: Hard: The Fifth Part  Feb 14th, 2021, 6:01am 
Started by alien2 | Last post by towr
That would make it a lot easier, yes. I mean, it gives away 86% of the answer.
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 10   riddles / what am i / Re: A Key Without a Door  Jan 26th, 2021, 4:27am 
Started by alien2 | Last post by alien2
I am baffled and bedazzled, as always. Still, I am convinced that you nailed it, in your own way.
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