## Puzzles

The absolute value of a real number is defined as its numerical value without regard for sign. So, for example, abs(2) = abs(-2) = 2. The maximum of two real numbers is defined as the numerically bigger of the two. For example, max(2, -3) = max(2, 2) = 2. Express: (a) abs in terms of max; and (b) max in terms of abs. [...]

Wed, Aug 08, 2007, Continue reading at the source

Lagrange's Four-Square Theorem states that every positive integer can be written as the sum of at most four squares. For example, 6 = 2^2 + 1^2 + 1^2 is the sum of three squares. Given this theorem, prove that any positive multiple of 8 can be written as the sum of eight odd squares. [...]

Wed, May 23, 2007, Continue reading at the source

By Fermat's Little Theorem, the number x = (2^(p-1) - 1)/p is always an integer if p is an odd prime. For what values of p is x a perfect square? [...]

Thu, May 10, 2007, Continue reading at the source

Compute the infinite product [sin(x) cos(x/2)]^(1/2) * [sin(x/2) cos(x/4)]^(1/4) * [sin(x/4) cos(x/8)]^(1/8) * ... , where 0 [...]

Fri, May 04, 2007, Continue reading at the source

Find all positive real solutions of the simultaneous equations: x + y^2 + z^3 = 3, y + z^2 + x^3 = 3, z + x^2 + y^3 = 3. [...]

Fri, Apr 27, 2007, Continue reading at the source

Money Talks
Do you listen when money talks? There are many phrases and sayings that talk about money. Speaking of money, see how many of these phrases you can figure out. Take the Quiz at Braingle.com
[...]

Sat, Oct 20, 2018, Continue reading at the source

Icebreakers are little exercises that help relax tensions and loosen up a formal atmosphere in a meeting where you want to have creative ideas and group participation.
The "Visual Puns" game is a fun activity that gets people thinking creatively. Pick an ordinary object such as a stapler or trashcan. As you pass the object around the room, each person must think of something that the object looks or acts like. For example, a stapler could be an alligator, some castanets or a catapult. A trashcan could be a hat, a soup bowl or a swimming pool for a beetle. Let your imaginations run wild and encourage wild ideas.
[...]

Sun, Oct 21, 2018, Continue reading at the source

A repressed memory is one that is still stored in the brain, but is not accessible by the conscious mind. Because these memories are usual of traumatic events, the theory is that the mind represses them to protect the individual from undue psychological stress. When a repressed memory is brought back into consciousness, it is called a recovered memory.
Due to the relative ease with which a practitioner can intentionally or unintentionally implant false memories via the power of suggestion, there is currently a great debate among psychologists as to whether or not repressed memories actually exist.
[...]

Sun, Oct 21, 2018, Continue reading at the source

A New Type of Word Pyramid
In this word pyramid you have to take the letters from the word pea and put them around the 'h' to form a new word. Once you have the next word, do the same with the next line.
pea
h _ _ _
s _ _ _ _
_ _ r _ _ _
_ _ _ _ _ _ n
_ _ _ _ _ _ _ l
Check Braingle.com for the answer.
[...]

Sun, Oct 21, 2018, Continue reading at the source

The Olympian Family Tree - Athena
The Olympians were the major gods and goddesses of Greek mythology. Their family was dysfunctional, to say the least, with enough adultery and incest to fill any daytime talk show. How much do you know about Athena and her relations? Take the Quiz at Braingle.com
[...]

Sun, Oct 21, 2018, Continue reading at the source

in-vo-lute
adj :: Intricate or complex.
"The possible moves being not only manifold but involute, the chances of such oversights are multiplied; and in nine cases out of ten it is the more concentrative rather than the more acute player who conquers." --Poe, Edgar Allan
[...]

Sun, Oct 21, 2018, Continue reading at the source

Trios
The following 15 words can be divided into 5 groups of 3 words. The words in each trio will share a similar characteristic. What are the groupings? Why?
astern, bony, con, deal, land, lien, nit, pending, pinion, range, slander, steroid, tile, vary, venue
Check Braingle.com for the answer.
[...]

Sat, Oct 20, 2018, Continue reading at the source

Deck The Halls...
Put your Christmas carol knowledge to the test! Take the Quiz at Braingle.com
[...]

Sat, Oct 20, 2018, Continue reading at the source

pro-pi-ti-a-to-ry
adj :: Conciliatory, appeasing or mitigating.
"Even the propitiatory gestures of the creature failed to disarm me." --The Island of Doctor Moreau by Wells, H.G.
[...]

Sat, Oct 20, 2018, Continue reading at the source