BrainDen.com - Brain Teasers

# bonanova

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6966

65

1. ## Distorted rectangular prism

Are we looking at the back and front 4x4 faces from the same direction? Or, does left and right, as they refer to the back face, assume we have turned the shape around so we're looking at outside of the back 4x4 face? That is, if we label the vertices ABCD on the front face, clockwise starting from the upper left corner like this A B D C Then if the 8" edges connect these to the back face vertices EFGH as A-E, B-F, C-G, D-H would your connections be A to H, D to G, and so on? It sounds as if we are joining the front and back faces of a prism to form a torus that has a square cross section, only we're twisting the shape by 90 degrees before joining the faces. (Kind of like constructing a Mobius strip from a piece of paper. This new shape would have only three sides, just as a Mobius strip has only one side. Interesting.) I wonder, though, with the length (8) being only twice the side (4) whether this is even possible. One thought:
2. ## Mega Einstein Riddle

I noted the number(s) of the clue(s) that refer to each of the items. This is making it easier to piece together little clusters of relationships. Next I'm trying to fit these clusters into a table where one column is filled in (e.g. house numbers). Or probably into several tables, each with a different column filled in, depending on the "shape" of the clusters. It's a huge puzzle any way you look at it.
3. ## Mega Einstein Riddle

Thanks for the category lists and clarifications. This is actually a favorite style of puzzle, and I can see myself enjoying it for a while. @Thalia, Game on ...
4. ## Find the number

You are given the following ten statements and are asked to determine a particular number. At least one of statements 9 and 10 is true. This either is the first true or the first false statement. There are three consecutive false statements. The difference between the numbers of the last true and the first true statement divides the number. The sum of the numbers of the true statements is the number. This is not the last true statement. The number of each true statement divides the number. The number is the percentage of true statements. The number of divisors of the number (apart from 1 and itself) is greater than the sum of the numbers of the true statements. No three consecutive statements are true. What is the number ?
5. ## my conjecture

@mmiguel, Nice.
6. ## Mega Einstein Riddle

@rocdocmac, Challenging puzzle! Clearly you spent some time on it. @Thalia, your questions (and the answers) were helpful. BTW, are you giving up on the puzzle? Have you listed all items by category yet? I'm in that process now, as a first step, before making a grid. Comments Assumptions: (just mention the ones that might be wrong) Questions:
7. ## The complexities of love

Eight young people met at a party. After the revelry, each had fallen in love with one of the four persons of opposite gender and came to be loved by another of those four. Here are the particulars. John fell in love with a girl who is, unfortunately, in love with Jim. Arthur loves a girl who loves the man who loves Ellen. Mary is loved by the man who is loved by the girl who loved by Bruce. Gloria hates Bruce and is hated by the man who is loved by Hazel. So ... Who loves Arthur?

9. ## Mega Einstein Riddle

For convenience I'll post the puzzle here in text form.
10. ## Mega Einstein Riddle

Certainly. Let me know if you have any difficulty.
11. ## Powerful rational number?

Can you find irrational numbers a and b such that ab is a rational number?

13. ## Folding paper

Agree. When I hit the send button, I realized my thinking was too simple. But instead of deleting my post (moderator privilege) I left it to take its licks.

15. ## Escaping the train

I agree. I put it into his post.

17. ## Cutting yet another cake

You are correct. But where shall the cut be positioned? Probably four. One for each side
18. ## Cutting yet another cake

Good question. Not similar. Not congruent. Just equal area (viewed from top) any shape.

Meanderings.
20. ## Escaping the train

A man walking home takes a shortcut through a train tunnel. A quarter of the way in, he hears a train whistle behind him. The tunnel is not wide enough for the man to escape being hit by the train, so he must either turn back, or go forward, at his top speed of 20 mph. Either way he will escape, but by the slimmest of margins. How fast is the train moving? All correct solutions will be accepted. The coveted bonanova Gold Star will be awarded for a solution that can be explained in words only, without equations or algebra. (e.g. without saying, "Let T be the speed of the train and D be the distance of the train from the tunnel, then t = D/T is the time that the man has in order to ..." etc. )
21. ## Cutting yet another cake

You are to cut rectangular cake into two pieces of equal size, but a rectangular piece of the cake has already been removed. Your cut must be a single straight cut. (Because the cake is frosted, a horizontal cut won't work. One piece won't have any frosting.) How would you do it? Assume the cake has constant thickness, so the problem is the same as cutting a rectangular piece of paper with a rectangular portion already removed.

23. ## The lion and the tamer, Part 2

@plasmid, That's an interesting conjecture - that the lion would catch the tamer iff x=0 (in your notation.) A while back, on another computer whose drive crashed, I simulated the 45-degree case (of a dog chasing a fox, I think, but that doesn't matter) and I don't think the fox was caught. I don't recall finding an angle where there was a capture. I think I'll re-write the program. It's not hard to simulate the chase, and you can get arbitrarily close to the exact solution by decreasing the time increment. ----- OK, I searched images the site has stored from previous postings. I found this one, showing a (blue) fox starting from the origin and following various radial paths. A (green) dog starts from (-1, 0) and traces the (green) pursuit paths. The figure does not seem to indicate whether there was a capture. Note this is not the original lion vs tamer situation -- the red circle is not a cage. In fact, it may have been a modified ogre-maiden situation where the red circle denotes a successful escape for the fox.
24. ## Circles and Chords a theory

Of course you're right. I needlessly put the chords on the same side of center.
25. ## Seeking Advise from Puzzle Masters

Hi Anthony, Do you envision having solvers come up with a single answer? That is, there is one particular virus, one particular set of <x> possible compounds, one particular value <y> for the number of slots, and therefore one particular ordered set of <y> compounds that will kill the virus? If so, then just give us values for <x> and <y> and we can work on it here. Or, will there be many instances of virii, with differing numbers for <x> and <y>, to be solved? If so, then what you need is an algorithm for generating clues. Or an algorithm for determining when a sufficient amount of random historical testing has been done to determine the 100% cure.
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