BrainDen.com - Brain Teasers

# bonanova

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6897

64

1. ## Circles covering a rectangle

This is another puzzle where precise wording is important -- I'll try to get it right, but if anything is unclear, please ask ... I'll start out by saying that all the circles in this puzzle have the same radius, the aspect ratio of the rectangle is not specified and does not matter, and its size, relative to the size of the circles is only indirectly implied. Only the constraints stated in the puzzle should be assumed. I've drawn 17 circles that at least partially overlap a rectangle. Their centers all lie within the rectangle. None of the circles overlap or even touch any of the other circles. There is no room for an 18th circle to be added to the group. That is, the circles are drawn in such a way that even though there is space between them, it is impossible to draw another circle whose center lies within the rectangle that does not at least partially overlap one of the first 17 circles. That is all you know about the relative sizes of things. And it is enough information to answer the following question: First, let's erase the circles that I drew. Then I will paint the rectangle red and give you a large supply of opaque white circles. What is the smallest number of circles you will need to completely cover the rectangle? (so that no red will be showing.) The centers of the circles, again, must lie within the rectangle, but now, of course, the circles can overlap each other, Edit: The puzzle can be solved as stated, but in order to guarantee the solution is the absolute smallest number, the following constraint is added to the original placement: The 17 circles were drawn as densely as possible without overlap. Thanks to @Molly Mae for raising this point.
2. ## Windows 10 -- Do you love it?

Amid a flood of contradictory comments about how good/bad Windows 10 is, I installed it on my notebook last week, In general I like it and don't see anything buggy or undesirable. What is your experience? Thumbs up or down?
3. ## Tiling a hexagon

A regular hexagon is divided into 2n equilateral triangles. Pairing triangles that share an edge produces diamond shapes with three distinct orientations, as shown. Prove that any n-diamond tiling of the hexagon will use the three types in equal numbers.

5. ## 12 RIDDLES THAT WILL TRICK YOUR MIND

I'll give these a shot.
6. ## Logic Puzzle with 26 Variables

Hi Tomson, and welcome to the Den. An oldie but goodie.
7. ## I'm not a bird

Poe, E. Near a Raven Midnights so dreary, tired and weary. Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap -- the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor. 'This,' I whispered quietly, 'I ignore.' - Mike Keith, 1995
8. ## Rodent Riddle

I watch word riddles in awe from the sidelines cuz my brain is wired deductively rather than inductively. On this one, tho, as a musician of sorts, I have to say, bravo! Great riddle and great solve!

OK thx.

FF?
11. ## I might be a writer

That's the answer I'm looking for. If you put your two posts together, you've got it.
12. ## Brain Teaser

Agree. If "Heidi" is the intended subject of "found," a 2nd "who" would serve no purpose except to confuse. It would not be used. Instead, Heidi is { immediately right of (Person A) } and found { more caches than (Person B) }. But since there are two "who"s, it's proper to bind them to the same (and closest) antecedent: ..... (Person A) { who has flown ... } and { who found more ... } 7) Heidi is immediately right of the person who has flown over from the States, and who found more caches than the UK cacher. 40 Traditional cache where found by a European cacher, their favourite type. Agree. They could not be Pitches 3 and 5, for example. I also fixed a typo in my interpretation post.
13. ## Square Free

Clarification:

15. ## Brain Teaser

My interpretations I believe gives this solution

17. ## Brainden races

At the annual Brain Denizen picnic, there were the inevitable games, among them the ever-popular three-legged race. Three teams were formed by tying one contestant's right leg to another' s left leg. Fortunately all six contestants made it to the finish line without any broken bones! For purposes of this puzzle we assume all three teams ran the 100-meter course at constant speed. Team 2, comprising BMAD and Thalia, were able to beat Team 3, comprising rocdocmac and DejMar by 20 meters, but lost to the winner, Team 1, comprising plasmid and plainglazed, by 20 meters as well. By how many meters did Team 1 beat Team 3?
18. ## I might be a writer

Yes, sir, that is exactly the right track.
19. ## One Girl - One Boy

They are equally likely but they are not the same. But it's worse than that. The OP is deficient, because it does not tell us how we came to know what we know. Instead, let's create a situation where we know how we know what we know, and therefore will let us find the probability that "the other kid is a girl," unambiguously. Doing that, we know the answer is 1/3.
20. ## Crypto-anagram

So, while not being a correct solution, this would meet that qualification?
21. ## Crypto-anagram

Once letters start getting removed it quickly gets easier. At the start it's very hard. How much of a clue are you willing to share? I don't want to disclose too much, but would you be willing to confirm the politician is male and contemporaneous? Initials or country of affiliation might be too revealing.
22. ## the distinguished matrix

This sounds a lot, but not exactly, like eliminating variables from sets of equations. Is that the idea?

24. ## Brainden races

Both answers state correctly that (a) winning distances give speed ratios and (b) combined speed ratio gives combined winning distance. What part of that can be more (or less) straightforward?

Kudos.
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