BrainDen.com - Brain Teasers

# bonanova

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62

1. ## If you are honest...

How about... "Do you refuse to answer this question"? If he answers "Yes," he lies. If he refuses to answer [attempting an affirmative response] he hasn't answered "Yes". Melchang, are you saying this question can, at some point be answered yes, according to situations and environments?
2. ## Does the plane take off?

Answer for a jet: Yes. Answer for a propeller plane: Yes. Reasoning: An airplane takes off when its wings generate a lift force greater than its weight. Lift force is determined by air speed. A backward-running treadmill will not impede the plane's forward motion, nor limit its air speed, only make its wheels spin twice as fast! But what if an airplane's engine drove its wheels? Then the answer would be No. It could not achieve forward motion nor generate lift. That would be an interesting kind of airplane - after it took off it would become a glider!
3. ## Place 4 dots in a plane

For the 2nd 3-3 solution here is a hint: What if there were 5 points to be placed? Here are the solutions:
4. ## Hole in a sphere

Very nice! There are two steps to get to 36pi. [1] deducing it doesn't depend on R. [2] computing the R=3 case. Step [1] can be done logically or mathematically. Wordblind absolutely wins the prize for the slickest math.
5. ## The Hill

Verifying Martini's result ... The order on the hill is always [D W J] The positions, and Jenkins' distance, at 7 critical points are as follows: 0. Start at the bottom [0 0 0 => 0] then ...
6. ## Take me there

Plausible, reasonable and simple. Compelling, even. Oh wait. The problem states: "This bridge capacity is up to 80 kgs only, if you exceed this limit the bridge will fall". "up to 80 kg only" [an open interval] does not include 80. Therefore "a perfect 80kg" "exceed this limit," and so "the bridge will fall."
7. ## Literarily thinking

That part matters most.

Correct
9. ## Literarily thinking

If two speak the same language, have access to similar dictionaries and understand rules of grammar and syntax, then we say they can communicate in a literate manner. The meaning of words is a mixture of the "dictionary meaning" and the personal experience of the speaker and listener. The latter component of meaning leads at times to misunderstanding until the context is communicated and understood. Culture and environment can alter generic meanings of words. How can we prove a word has a meaning? One approach might be to agree on a common dictionary as the authority. A more pragmatic approach might be to say that if two people are comfortable with the notion that they agree when they discuss something, then the words they used to reach agreement themselves have an agreed meaning. Is this what you had in mind?
10. ## Place 4 dots in a plane

Yup. I didn't want to describe the "found" ones yet - it's fun to find them, as well.

12. ## Cross the 3 Couples

Your solution avoids that situation. I think you solved a more difficult problem than was proposed. I opted for my approach because [1] It takes one fewer crossing [2] I believe the conditions provide for a momentary situation where a woman is without her husband but with another man, so long as she does not remain that way when the boat leaves them. Maybe the author can resolve whether my interpretation is permitted.
13. ## Cross the 3 Couples

You can't do it taking one at a time, and taking them two at a time is trivial. So I'll answer the problem of how they do it themselves. [edit - one of my letters was wrong] xy cross, x returns --- .. .y .. || Ax B. Cz Ax cross, A returns -- .x .y .. || A. B. Cz Cz cross, C returns -- .x .y .z || A. B. C. AB cross, z returns - Ax By .. || .. .. Cz Cz cross ------------- Ax By Cz || .. .. ..
14. ## Cross the 3 Couples

Please clarify - As you take them across the river, there can be no more than one of them with you in the boat?
15. ## Honestants and Swindlecants VII.

You're exactly right, I got it backward. Thanks for clarifying.
16. ## The Obtuse Family takes a vacation

Who are the three cousins in that case?

18. ## Hole in a sphere

I intuitively knew what the answer would be, but I have been struggling to come up with the mathematical proof of it. Looking at your math, though, I am puzzled. How do reason that the area of hole's cross-section (r*r) equals the area of the sphere's cross-section (R*R) less the the square of half the hole's length? R*R = r*r + L*L because you can draw a right triangle where R is the hypotenuse [Pythagorus]. Hint: slice the thing along the hole's axis running vertically. Go from the sphere's center horizontally to the surface of the hole - that's a distance r. Go straight up to the top of the hole - that's a distance L [at right angles to r] Go back to the center of the sphere - that's a distance R and is the hypotenuse. When I answered her question, I hadn't proved 36pi is true for all spheres. I just guessed. [it's really a quite surprising result!] But, for all she knew I did all this math in my head in 15 seconds! We were colleagues, and I would place her IQ somewhere north of 160 - high enough to think it could be done, and ... high enough that she usually left me in the dust in our work. She was impressed. It was an moment to savor, and I thought I'd share the story.
19. ## Hotel Bill

Here's another variation. A man took his bride to the same hotel the next night. When he settled the bill in the morning the clerk said that will be \$9 apiece. The man dutifully paid \$81 and left, mumbling to himself. Why?
20. ## HOTEL BILL

There's \$25 in the till, \$3 went back to the men and \$2 went to the clerk. 25+3+2=30. Here's a related puzzle. A man took his bride to the same hotel the next night. When he settled the bill in the morning the clerk said that will be \$9 apiece. The man dutifully paid \$81 and left, mumbling to himself. Why?
21. ## COMES NEXT

Since "ought" is alt spelling of "aught" carrying the meaning of "naught" or stretching it a bit "zero" then the sequence is initial letters of zero [ought] one two three four five six seven, and proceeds with E N T E T ...
22. ## Three Ants...

Ants don't need gravity, they stick. They took a circular [ok, triangular] path on the ground that slowly made its way up hill. At the top, they stayed in formation, pointed left, and said "he forgot the picnic!"
23. ## Hole in a sphere

Writersblock, Still laughing ... I love it! My only reply is ... ok I have two replies ... [1] she never complained and [2] the [apparently lacking] size spec is an important part of the logical solution.

25. ## Take me there

Doing the math and explaining that downward forces are needed to produce upward acceleration, etc. is absolutely correct; even tho the numbers change depending on how, and how high, he throws them. One might be tempted to suggest he could throw them very gently upward ... this approach fails, but more math is needed to prove it. A general argument states: If the total weight of the juggler and the watermelons is NOT being supported by the bridge [the only supporting structure present] then some or all of them will fall, and juggler will fail to get them across. Thus, the bridge DOES support the entire weight, and juggling is seen not to be a solution. ... unless ... the bridge is so short he can toss them into the air before getting on the bridge -- and catch them after he has finished crossing it.
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