BrainDen.com - Brain Teasers

# bonanova

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1. ## 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.
2. ## 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 || .. .. ..
3. ## 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?
4. ## Honestants and Swindlecants VII.

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

Who are the three cousins in that case?

7. ## 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.
8. ## Place 4 dots in a plane

If you connect all pairs of 4 dots in a plane [geometrical, not air] you create 6 line segments. This puzzle asks how many ways 4 points can be arranged such that the lengths of the 6 connecting lines share no more than 2 values. The points must be distinct. None of the lengths can be zero. Example: the corners of a square. The 4 sides and the 2 diagonals share common lengths: a so-called 4-2 solution. A moment's reflection and some equilateral triangles reveal there are at least 2 other 4-2 solutions, a 5-1 solution and a 3-3 solution. The real stumper is to find one more 3-3 solution - two in all. You can describe these in words, or attach a graphic. [This question was posed to Jr-High school students in a national competition.]
9. ## 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?
10. ## 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?
11. ## 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 ...
12. ## 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!"
13. ## 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.

15. ## 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.
16. ## Whatchya Gonna Do (2 goats and a car)

edit: ha! now I've read Riddari's first spoiler. This post adds nothing to what he said. The way I finally understood the answer is this: That one of the two doors you get by switching has a goat is a red herring. you knew that already. Doesn't change your chances. Riddari's explanation #2 is compelling, also - it's the same situation, magnified, and makes intuition favor the correct answer. It took me an hour to believe the 1 of 3 case.
17. ## Hole in a sphere

I did the calculus afterward, and however you do the calculation, it's difficult. The remaining volume is a volume of revolution with requires finding the cross sectional area and spinning it thru 360 degrees. It's no easier to compute the cylindrical volume removed, cuz there are spherical "caps" on the cylinder which don't have formulas that I could find. The logical way is easier, and I'll post it in a day or so if you don't get it... have fun.

Yes.
19. ## Hole in a sphere

Clarifications: [1] the hole is a circular cylinder of empty space whose axis passes through the center of the sphere - just as a drill would make if you aimed the center of the drill at the center of the sphere and made sure you drilled all the way through. [2] the length of the hole [6 inches] is the height of the cylinder that forms the inside surface once the hole is drilled. picture the inside surface as viewed from inside the hole and measure the length of that surface in the direction of the axis of the drill. in this sense, you could for example drill a 6-inch hole through the earth. the diameter of the hole would be huge, and you'd just have a tiny remnant of the earth left. but if you could set it on a table [a big table] it would be 6 inches high. you of course could not drill a 6-inch hole through a sphere whose diameter was less than 6 inches. it was actually this fact that led me to the logical answer and made me a genius for a couple of minutes.
20. ## Two easy ones.

He says, "I am lying." Which doesn't have a truth value.
21. ## Hole in a sphere

Maybe this has already been posted. A friend asked me this a while back, and I answered her in less than a minute. She said I was a genius. But I said there were two ways to arrive at the answer, and I simply chose the easier way. A 6-inch [long] hole is drilled through [the center of] a sphere. What is the volume of the remaining portion of the sphere? The hard way involves calculus. The easy way uses logic.
22. ## Romance and the Railroad

Riddari, You're correct on both comments [physical attributes and spoiler for mistake.] Thanks ... !
23. ## Nessie

I'm missing something. What rule is being broken?
24. ## Who were those masked men?

A variation on the Lone Ranger theme: A man left home one day and began to run. After he'd gone a ways, he turned left and kept running. A bit later he turned left again and ran a little faster. Later on, he turned left a final time and ran even faster than before. In the distance he saw two masked men. Who were they?
25. ## Typists problem

I first heard it posed as ... if a hen and a half can lay an egg and a half in a day and a half, how many hens would it take to lay 18 eggs in 3 days? It's tempting to figure a hen can lay an egg a day so it would take 6 hens. But it takes a hen and a half to lay an egg a day, so it takes 9 .
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