bodner088

While strolling through cyberspace via search engine , I came across some nifty word problems involving mixtures or solutions . These are my favorite types of algebra problems because there solutions require solutions. I can't seem to get enough irony (or wordplay) - I might be anemic. These are great problems to try to do in your head (visualize containers and the pouring process) if the math is easy enough. There are great fun, highly gratifying, and wonderful brain-trainers -- not only for algebraic reasoning, i.e., find the missing number, but for improving your ability to visualize.  That's right. The Braintenance Blog is offering our adherents (those who stick with us or to us) two benefits for the price of one. In fact, if we wanted to keep this sale in proportion we'd have to offer four benefits for the price of two; or three benefits for the price of one and a half; or (let's get crazy) one whole benefit at half price... do you see where I'm going? Here...

Image via Wikipedia  In our last thrill-packed episode of Braintenance , we discussed the benefits of doing arithmetic calculations ("chain calculations") without the assistance of computers or any extrasensorial visual aids. The problem in the re-posting of the last show, yielded an answer of 28 [or at least it should have]. Most people's biggest challenges are not the arithmetic at all -- the challenges are 1 ) memorizing a string of data, and 2 ) recalling the string in "pieces" ("fractional recall") when going back to check or reaffirm our computations . One hint which might prove helpful is to visualize the entire string as if it were placed at the top of your mental blackboard for reference, and to do the individual calculations below. In this way, you can trick your mind into having a source of embedded reference to go back to. By doing this, you'll have less problems worrying about 'losing your place,' during the computational pro...

When we utilize computers and other visual aids to do arithmetic calculations, several of our cognitive and computational abilities atrophy. We must exercise them in order to keep them strong. The simple process of doing arithmetic in your head allows you to visualize and to memorize. Many studies have shown that this rather simple exercise is one of the best ways to delay the onset of dementia and a number of other physiological manifestations of diminished mental capacity . Do the following example in your head...no using fingers to draw in the air, or using of any other external physical processes (especially whispering the numbers to yourself0. I'll get you your answer tomorrow. Go ahead. Try this simple one [by the way, you'll actually find it confusing to look at the numbers on this page at the same time you visualize the computations in your head. With practice, this problem can be eliminated by simply taking a mental "photograph" of the numbers, closing your ...

In performing simple arithmetic operations , a sign is required between two numbers to show what action is intended...you've seen the plus symbol, the minus symbol, the multiplication symbol and the division symbol. What follows is a quick Braintenance puzzle, designed to help you make use of several of your mental abilities simultaneously. The principal ability most of us default to is a very rapid trial and error -- when this is done with extreme speed by a computer, it is termed "brute force." Yet this brute force, when exercised in Humans (most of our readers are Humans, some are likely aliens monitoring our internet activity from their home planet, as they plan to conquer us -- but let's not get distracted), improves in terms of its speed. It is like Dran-o for the Brain-o. Find the missing signs which are all represented below as the letter "n" in the following simple equations. I'll have answers for you within the next two days. You have plenty o...

Image ( somewhat distracting and annoying ) via Wikipedia Progress, from the starting line to the finish line , can occur in many different ways. Some start the race slowly but speed up toward the end, using reserves of strength; some jog along at a steady, even pace; still others virtually go into orbit at the start and burn out quickly to a vomitous, spleen-gripping, huff-and-puff walk. Since we are Braintenance , we will choose a five kilometer race, in which three mathematicians are competing. Each has a distinct running pattern, strategy or (ulp!) formula for spanning the distance. The question to answer regarding each runner is simply this: "How long will it take him (in minutes ) to reach the finish line to receive his souvenir Tee-shirt?" Of course, these Ts are only available in one size...XXL. Here's the lineup of our contestants : Racer 1 :  This fellow runs (on average) one kilometer every 18 minutes. Racer 2 :  This fellow starts the race at a rate of one ki...

Image (somewhat distracting and annoying) via Wikipedia Progress, from the starting line to the finish line , can occur in many different ways. Some start the race slowly but speed up toward the end, using reserves of strength; some jog along at a steady, even pace; still others virtually go into orbit at the start and burn out quickly to a vomitous, spleen-gripping, huff-and-puff walk. Since we are Braintenance, we will choose a five kilometer race, in which five mathematicians are competing. Each has a distinct running pattern, strategy or (ulp!) formula for spanning the distance. The question to answer regarding each runner is simply this: "How long will it take him (in minutes ) to reach the finish line to receive his souvenir Tee-shirt?" Here's the lineup of our contestants : Racer 1:  This fellow runs (on average) one kilometer every 18 minutes. Racer 2:  This fellow starts the race at a rate of one kilometer every 12 minutes, but his pace declines by 10% per kilom...

Your mind is a muscle. You must use it to strengthen it. If you don't, it will atrophy and hasten your descent toward dementia (which is not the name of a town in the Midwestern USA ). Following are a pair of practical problems involving Pizza, Pi and Packaging . Try 'em. Background : Fabian Focaccia (not his real name, which is Sal Monella)  is a struggling 'artist' who is working at a neighborhood pizzeria in Brooklyn, New York (not his real location, as he is in the Federal Witness Protection Program , but which is still the best geographical location to make a pizza purchase if you/ youse should ever get around to it) to pay his bills until he can sell one of his paintings. He is faced with a decision and needs your help. He has cardboard boxes for 'take out' pizza (this pizza parlor does a big take-out business -- even for Arizona...oops!) which are each three inches deep (irrelevant for solving this problem) and measure exactly 20 inches by 20 inche...