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

Alcohol brain damage shoud be avoided, but many of us find it hard to say when. These are some of the brain dangers of drinking too much. [...]
Tue, Sep 02, 2014, Continue reading at the source
Check out all our free brain teasers here in one spot! All of them with answers. [...]
Sun, May 27, 2012, Continue reading at the source
Brain Tumor Warning Signs should not be overlooked. Early detection of a brain tumor may be difficult but we'll arm you with what to look for! [...]
Sun, May 27, 2012, Continue reading at the source
Chewing gum stimulates the brain! Your teacher didn't know what she was doing when she asked you to spit out your gum before class. [...]
Sun, May 27, 2012, Continue reading at the source
These are the early symptoms of brain cancer. If these match what you're feeling, be careful and contact you doctor immediately! [...]
Sun, May 27, 2012, Continue reading at the source

Literary Geography There are many literary works that have place names (both real and fictional) in their titles. This quiz will test your knowledge of those titles. Take the Quiz at Braingle.com [...]
Mon, May 21, 2018, Continue reading at the source

My first is how you feel on a day that's happy and bright. My second forms a landscape of stones, black and white. My third, a song like "Row Your Boat", but not like "Silent Night". My whole will take you nowhere, but fill you with delight. What am I? Check Braingle.com for the answer. [...]
Tue, May 22, 2018, Continue reading at the source
I am a parent but I have never given birth. I am very rarely still, yet I don't move. I am clothed in the warm and naked in the cold. What am I? Check Braingle.com for the answer. [...]
Tue, May 22, 2018, Continue reading at the source
Looking at the 3 "equations" below, what is the answer to the 4th one? 8 + 2 = 16106 5 + 4 = 2091 9 + 6 = 54153 7 + 3 = ? Check Braingle.com for the answer. [...]
Tue, May 22, 2018, Continue reading at the source
no room for ________ ________ing Thomas benefit of the _______ Check Braingle.com for the answer. [...]
Fri, May 18, 2018, Continue reading at the source
My first is lifted by mechanical power My second makes an impatient one's mood sour My whole makes one hit the sack at a strange hour What am I? Check Braingle.com for the answer. [...]
Thu, May 17, 2018, Continue reading at the source

The next time you are stuck on a project ask yourself this question, "If the goals of this project were completely opposite of the actual goals, what would I do differently?" When we think about a project in one particular way we can get into a mental rut which is hard to escape. A question like this gets you thinking about opposites, which will in turn get you out of the rut and get your mind thinking about new ideas. Sometimes solutions that are completely opposite of the solutions you seek can be very fruitful. [...]
Tue, May 22, 2018, Continue reading at the source
In the middle of the brain, connected to the cortex, is the hippocampus. Actually there are two hippocampi, one on each side of the brain. The hippocampus helps to form new memories about experienced events. It interprets incoming sensory inputs and turns them into memories. If the hippocampus is damaged, it becomes incredibly difficult to form new memories and recall old memories. In fact, it is one of the first parts of the brain that succumbs to Alzheimer's disease. The hippocampus also stores and processes spatial information. This is how you remember locations and know how to get from place to place. The types of people who never get lost and are good at finding shortcuts have a very active hippocampus. Taxi cab drivers tend to have a large hippocampus, indicating that if you use your spatial skills, your hippocampus can actually grow. To prevent information overload, your hippocampus is constantly sifting through incoming sensory inputs and deciding what to save and what to discard. For a memory to get into long-term storage, it must be selected by the hippocampus. Information with emotional significance or information that relates to something we already know tends to get preferential treatment. This is why meaningfulness is important for information you want to learn. [...]
Tue, May 22, 2018, Continue reading at the source
Words With YO Six words that contain YO as a letter-pair have had all of their other letters removed and placed into a pool. Put those letters back in their proper places. What are the words? YO---, YO----, -YO---, --YO--, ---YO-, ----YO Pool: A, B, B, C, C, D, D, D, E, E, E, E, I, L, M, M, N, N, N, N, P, R, R Check Braingle.com for the answer. [...]
Tue, May 22, 2018, Continue reading at the source
Roman Numerals Do you know your Roman Numerals? Take the Quiz at Braingle.com [...]
Tue, May 22, 2018, Continue reading at the source
ped-ant noun :: One who makes a show of knowledge. "John is an annoying pedant who bores people with his useless facts." [...]
Tue, May 22, 2018, Continue reading at the source
Just as your subconscious can work on problems while you do something else, your subconscious can also work on a task while you sleep on it. Here is an exercise to help you prepare to sleep on a problem. Get a piece of paper and write down a one-sentence summary of your problem or project. Then write down a few related keywords. Review the problem in your mind for a few minutes and make a conscious request to yourself to think about this problem while you sleep. Now, forget about it and go to sleep. As soon as you awaken, look at the piece of paper and read the summary and keywords. Chances are, some interesting ideas will come to mind. Write these down and review them later. You may find that the answer to your problem has come to you in your sleep. [...]
Mon, May 21, 2018, Continue reading at the source
The cerebral cortex is the main part of the human brain. It is the part that handles memory, language, thought, and consciousness. When you see a picture of a brain, the outer layer that looks convoluted and bumpy is the cerebral cortex. It is actually a flat sheet of cells that are all bunched up around the middle parts of the brain. This folding increases the surface area; if you unfolded a human cortex, it would measure more than 4 square feet. The cortex is made up of four lobes separated from front to back and left to right. Each type of sensory input has its own place on the cortex. For example, there is a specific place where all processing related to smells happen. Muscle movements have their own spot, vision has a spot, and so on. [...]
Mon, May 21, 2018, Continue reading at the source
1000 Word Essay A boy was in detention from talking too much when the teacher was talking. The detention teacher said, "You have to produce a 1000 word essay in 30 seconds...GO!!" The boy actually did it. How? Note: he did not just write "A 1000 word essay" on his paper. You'll have to be a little more clever than that. Check Braingle.com for the answer. [...]
Mon, May 21, 2018, Continue reading at the source
Princess Diaries How much do you know about this movie? Take the Quiz at Braingle.com [...]
Mon, May 21, 2018, Continue reading at the source
in-sip-id adj :: Lacking in qualities that interest, stimulate, or challenge. Dull. "Although his early poetry seems insipid, his later work is more interesting." [...]
Mon, May 21, 2018, Continue reading at the source