# Forums

1. #### New Logic/Math Puzzles

They can be logical [e.g. honestans/swindlecants or hats on death row], math [e.g. probability, sequences], physics or geometry, especially where intuition might suggest wrong answer.

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2. #### New Word Riddles

Inductive, intuitive, but still requiring some thought (eg. riddle of the sphynx, What-Am-I riddles, anagrams, Shakeepuddn's style, etc.)

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3. #### New Optical Illusions

Post amazing illusions you have seen on the web right here.

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4. #### Other Mind Boggling Stuff On Web

Anything else on the web that is worth mentioning.

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1. #### Puzzles and Riddles (section closed)

My favorite puzzles sorted in several subforums.

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The most famous paradoxes - liar paradox, barber paradox, doubtful existence of God, sentences from life, and sophisms.

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3. #### Brain Games and Others

Hints and help from other visitors.

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1. #### Games

Join mostly role playing games played over several days (eg. Mafia game).

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2. #### Homework Help

This forum is for homework HELP.
DO NOT do others homework for them.

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3. #### Jokes

Do you know a good joke? One that is appropriate for kids as well? Share it with the world - post it right here.

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Your feedback on what to improve and any questions regarding BrainDen.

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5. #### Others

Share your thoughts on anything else not mentioned in other categories (eg. you can discuss philosophy related questions).

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6. #### Introduce Yourself

If you want to say hello, share how you got here and what you are looking for in BrainDen forums, then this is the place to do it. One thread per member please.

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• ### Posts

Posted · Report

Fun with real numbers

For part I.

I get K=9.

The inequality holds for K=0.

Assume there is a largest K for which the inequality holds for all 0 <= a <= b <= c <= d. Then for some a=0, b=c=d > a= 0 we get (a + b + c + d)^2 >= K b c <=> (3d)^2 >=Kd^2. Since d>0, this means K<=9.

For all 0 <= a <= b <= c <= d the following holds true:

(a + b + c + d)^2 >= (0 + b + c + c)^2 = (b+2*c)^2 = b^2 + (2*c)^2 + 2*b*(2*c) = b^2 + c^2 + 3*c^2 + 2*b*c + 2*b*c =(b+c)^2 + 3*c^2 +2*b*c >= 4*b*c + 3*b*c + 2*b*c = 9*b*c.

Last step uses at once:

- (b+c)^2 >= 4bc which is equivalent to (b-c)^2 >=0

- 3*c^2 = 3*c * c >= 3*b*c since c>=b, c,b>=0

Equality holds for a=0, d=c, b=c.

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Posted · Report

Anagrams for Fun - I: Defintions?

3. The Morse Code

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Posted · Report

Anagrams for Fun - I: Defintions?

I'll get things started

1. Dormitory
2. Desperation
3. ??
4. Slot Machines
5. Animosity
6.  ??
7. Alec Guinness (only know that one from Simpsons!)
8. Semolina
9. ??
10. ??
11. ??
12. Eleven plus two
13. ??

A couple more...

10) Decimal Point

11) The earthquakes

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Anagrams for Fun - II: Quotations
1. In one of the Bard's best thought of tragedies, our insistent hero, Hamlet, queries on two fronts about how life turns rotten.

2. A thin man ran; makes a large stride; left planet, pins flag on moon! On to Mars!
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Posted (edited) · Report

Anagrams for Fun - I: Defintions?

An Anagram, as we all know, is a word or phrase made by transposing or rearranging the letters of another word or phrase. The following phrases can be anagrammed into their definition or description. Honor code is in force:

1. Dirty Room          (Clue: single word beginning with D.)
2. A Rope Ends It
3. Here Come Dots
4. Cash Lost in 'em
5. Is No Amity
6. Alas! No More Z's
7. Genuine Class
8. Is No Meal
9. Large Picture Halls, I bet
10. I'm a Dot in Place
11. That Queer Shake
12. Twelve plus one
13. Accord not in it

Edited by bonanova
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