BRAINTENANCE BREAK 1/20/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

Today was the inauguration of the 44th president of the United States Of America. In honor of this much-heralded event, I will post the solution to the last quiz tomorrow.

In the meantime, please scroll on up to find a new Warm-Up exercise: We are happy to present you with the GRE WORD OF THE DAY. We now have a 3rd warm-up exercise before we get into the tough stuff. Please give it a try. And remember to make this site a favorite.

A few moments of Braintenance per day can absolutely create wonders. Do this for yourself!

Faithfully,

Douglas Castle

p.s. How many combinations of 5 letters each can you make from "OBAMA" which do not begin with the letter "O"?

BRAINTENANCE QUIZ 1/19/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

If you combine math with imagination, you get problem-solving ability. The exercise du jour (goodness...have I spoken French?....no, I've written it), requires a bit of imagination and a bit of math. The type of thinking involved is very practical and worth cultivating.

Given: You have the bottles. One of them is a 2-gallon bottle filled with a 40% solution of hxdroxyidiotic acid (I have invented this substance); one is a 2-gallon bottle filled with water; one is a 4-gallon bottle, which is empty. You have access to additional water at a nearby pump.

Find:
1. How would you create 4 gallons of a 20% solution of hydroxyidiotic acid?
2. How would you create 2 gallons of a 20% solution of hydroxyidiotic acid?
3. How would you create 1 gallon of a 20% solution of hydroxyidiotic acid?
4. How would you create 2 gallons of a 10% solution of hydroxyidiotic acid?
5. How would you create 1 gallon of a 10% solution of hydroxyidiotic acid?

Good luck!

Faithfully,

Douglas Castle

______________________________________________________
Solution (no pun intended in light of the foregoing) to the last exercise:

If a person takes one step back for every two steps forward, it means that he or she only advances one step ahead for each two steps taken. This is actually a formula. If he or she were to take 20 steps in total, he or she would only have gained ten steps (i.e., be ten steps ahead) after having taken a total of 2o steps.

BRAINTENANCE QUIZ 1/16/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:


If an individual tends to take two steps forward, and then one step back, how many steps will he have advanced after having made a total of 20 steps (including both forward and backward)?


Faithfully,


Douglas Castle


______________________________________________________
Commentary on the last quiz:

You should learn at least one new word every day.
You should look up words which you do not know, instead of defining them "in context".
When you learn a new word, try to find several synonyms for it.
When you learn a new word, try to find several antonyms for it.
When you learn a new word, be certain to use it in at least five sentences that day.
_______________________________________________________

BRAINTENANCE QUIZ 1/14/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

You might wish to go to www.dictionary.com and use the Thesarus Feature to come up with at least 5 synonyms and 5 antonyms for the words which follow. In fact, you might wish to look some of these words up in the dictionary before you begin your work:

1. Freedom
2. Faith
3. catholic (lower-case "c")
4. Despise
5. Sophistication

Good luck!

Faithfully,

Douglas Castle
__________________________________________________
The answer to the last quiz:

Q: How far can a dog run into the woods?

A: Halfway, and then he is running out of the woods.
__________________________________________________

BRAINTENANCE QUIZ 1/14/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

I have but one question to ask of you.

How far can a dog run into the woods?

Faithfully,

Douglas Castle
_______________________________________________
Here are some answers to the last quiz:

1. What is the probability that no lightbulbs will go out?

The probability that any one lightbulb will not go out is .95 (which is 1.00 - .05). The probability that ten out of ten lightbulbs will survive the night would be (.95) (.95) (.95) (.95) (.95) (.95) (.95) (.95) (.95) (.95) = .60 or 60%

2. What is the probability that any one lightbulb will go out?

The probability that any one of the lightbulbs (it doesn’t matter which) will go out in the group of ten would be found by dividing .05 [the probability that any one single lightbulb goes out] by .60 [the probability that none of the lightbulbs go out], which would equal .08 or 8%. The mistake that many people make in working with this problem is that they will multiply (.95) times itself nine times, and then multiply that result by .05. This does not work, because each lightbulb operates independently of the others. The answer that you would obtain that way would be smaller than .05, which clearly would not make sense – intuitively, you realize that the answer doesn’t make sense if it is less than .05. Intuition is an important tool!

3. What is the probability that any two lightbulbs will go out (together)?

The probability that any two lightbulbs would go out together, i.e., jointly, would be (.05) (.05) or .0025, or .25%. Using the same reasoning as in the solution to the second problem above, we would obtain our answer by dividing .0025 by .60. The solution would be .000416 or .0416%. Intuitively, this also makes sense because the probability of two lightbulbs going out together should be smaller than the probability of only one lightbulb going out in the whole group.

4. What is the probability that up to three lightbulbs will go out?

This question is asking for the sum of the probabilities that: one lightbulb will go out alone; that two lightbulbs will go out together; and that three lightbulbs will go out together. To solve this one, we add the solution to the second problem (.08), to the solution to the third problem (.025), and then add (.05) (.05) (.05)/ (.60) [the probability of three bulbs going out together], and we get: .08 + .000416 + .000208 = .080624 or 8.06%. Intuitively this makes sense because the additive probabilities of all three cases would have to be a number greater than any one of the individual numbers.

5. What is the probability that either three or four lightbulbs will go out?

I am feeling exhausted and even a bit cantankerous. I’ll let you figure this one out yourself, while I have coffee. :)

BRAINTENANCE QUIZ 1/13/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:


Today's exercise is fairly easy, but you must read each question carefully in order to understand precisely what is being asked of you! Again: Read Carefully.


A room is lit by ten independently wired (and powered) light bulbs. The probability of a bulb going out during any given night is .05 or 5%. The questions which follow involve one particular night.



1. What is the probability that no lightbulbs will go out?

2. What is the probability that any one lightbulb will go out?

3. What is the probability that any two lightbulbs will go out (together)?

4. What is the probability that up to three lightbulbs will go out?

5. What is the probability that either three or four lightbulbs will go out?


Enjoy this exercise.


Before we get to our solutions to the last quiz, here's an article of interest (reprinted from INTERNAL ENERGY PLUS) that might provide you will an enjoyable stress-buster, as well as an introduction to the amazing power of the mind to manifest changes in physiology and mood.


Dear Friends:

As many of you know, I invest a great deal of time discussing some of the less-known but powerful Modalities (i.e., special tools and techniques) of INTERNAL ENERGY PLUS. One of them is Entrainment (re-programming your emotions through direct signalling to the brain), and another is Deliberate Breathing. These are the two which you can use, right now, to create an amazing, soothing, re-energizing effect.

*If you need a quick refresher (no pun intended) on breathing technique, please quickly re-view the most recent two or three posts on http://theinternalenergyplusforum.blogspot.com/ and http://douglascastleiep.blogspot.com/

*If you need some very fast information about Entrainment, go straight to our website at http://www.internalenergyplus.com/ . Look under the TOOLS Section.

Here's a stress-reduction exercise that works miraculously, and in less than five minutes:

1. Sit down comfortably in a quiet place. Close your eyes. Breathe slowly, deeply and deliberately for twenty breaths. If you do this properly, you will visualize negativity leaving your mouth like a cloud of ashes, and golden light entering your body with every refreshing, rich inhalation. Your muscles will relax. You will feel a bit lightheaded. Just focus on your breathing. Open your eyes, and stretch your back (still seated).

2. Click on the following audio clip (at a fairly high volume), close your eyes, and visualize a golden light running its course, up and down, repeatedly, from the base of your spine to the very top and center of your head...almost like a warming internal massage, clearing an energy pathway through your body.

http://www.mind-sync.com/sampler.mp3

After you have done this, you will have an amazing feeling of relaxed re-connection. Please post your comments and reactions. We are all interested.

Faithfully,

Douglas Castle

p.s. You might want to forward this little bit of heaven to a few friends and colleagues!
DOUGLAS CASTLE

THE NATIONAL NETWORKER- We Are Networking
BRAINTENANCE - Stay Razor Sharp
INTERNAL ENERGY PLUS - Human Potential
THE INTERNATIONALIST PAGE
THE GLOBAL FUTURIST
*****

_________________________________________________________
And now, the answers to the last quiz! The first two of these questions could be answered with good estimates and at warp speed by simply using the "Rule of 72". The rule states that "if you divide the annual interest rate (expressed as a percentage, and NOT A DECIMAL EXPRESSION) into 72, you will find out how many years it will take for your money to double". The rule further states that "if you divide the number of years into 72, you will find out the interest rate required in order to double your money." It's that simple!

1. How long will it take to double your money at 14.4% interest compounded per year? If we divide 72 by 14.4, our answer will be approximately 5 years.

2. At what interest rate, compounded per year, will it take to double an initial investment of $1,000.00 in 5 years? If we divide 72 by 5 years, our answer will be approximately 14.4%.

3. What sum must we initially deposit in order to accumulate the sum of $3,000 in 10 years at an annual compounded rate of 8.00%? Gosh, I feel moody today. Even a bit surly. I won't give you the answer just yet. Instead, I'll provide a hint: At the end of 1 year, the starting amount ("X") will have grown to X(1.08). At the end of two years, X will have grown to X(1.08)(1.08). Do you see a pattern???

Stay tuned!

BRAINTENANCE QUIZ 12/10/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

Here are some simple financial questions (answers may be approximate)

1. How long will it take to double your money at 14.4% interest compounded per year?

2. At what interest rate, compounded per year, will it take to double an initial investment of $1,000.00 per year in 5 years?

3. What sum must we initially deposit in order to accumulate the sum of $3,000 in 10 years at an annual compounded rate of 8.00%?

Good Luck!

Faithfully,

Douglas Castle
_________________________________________________________________
Answers to the last quiz follow:

Bob is 7 years old and Ray is 11 years old. The technique to solve this problem reuires some simple algebraic substitution and a knowledge of simultaneous equations. Hint: Ray's age is actually Bob's age + 4. This is really your easiest starting point.

BRAINTENANCE QUIZ 12/7/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

Today's quiz is quite simple:

1. Bob and Ray are brothers. Bob is younger.
2. They are 4 years apart in terms of their respective ages.
3. Their combined ages, in three years, will be 24.
4. The product (by multiplication) of their ages in three years will be 140.

Q: What is Ray's age now? What is Bob's age now?

Faithfully,

Douglas Castle
_________________________________________________________________
If you would like the answers to the last quiz, you will have to avail yourself of a dictionary. By the way, the word most often used improperly is "notoriety." It does not mean "fame"...it means "to be known for ill deeds, to be maligned, the state of being notorious". When your buddy says, "I want to make a hit record and achieve notoriety", he or she is misusing the term, unless the hit record is going to be very controversial or of poor quality.

BRAINTENANCE QUIZ 1/5/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

Can you define these words?

1. EUPHEMISM
2. SYNCRETIC
3. ENDEMIC
4. INDIGENOUS
5. NOTORIETY
7. LUGUBRIOUS

Faithfully,

Douglas Castle

p.s. At least one of these words is used improperly most of the time, because its definition is not well-known. Which one is it?

BRAINTENANCE QUIZ 1/2/09

Share this ARTICLE with your colleagues on LinkedIn .

---

Dear Friends:

Happy New Year!

There's no quiz for today. Your exercise is to invest some time in planning how to make 2009 the best year in your life's experience. I am hopeful that you will be dedicate some of this time to getting to know your inner-selves better, and to resolving to become brighter, better thinkers, and greater contributors to the Collective Body of Human Knowledge and Experience.

Faithfully,

Douglas Castle
____________________________________________________
Answers to the last two quizzes are posted below:


Assume (although we should not assume too often) that we have two men and two women whom we wish to seat in a row:


1) How many ways can these four people be arranged? In 24 different ways. The reasoning: There are 4 people to choose from to occupy the first seat; 3 people left to occupy the second; 2 to occupy the third; and 1 to occupy the last. 4x3x2x1 = 24 different possible arrangements.


2) How many ways can these people be arranged if they must be seated with people of the opposite sex seated next to eachother? There are four configurations for seating, which are MFMF, FMFM, FMMF and MFFM (where M = male and F = female). The computations for each configuration are 2x2x1x1 (=4 arrangments), 2x2x1x1 (= 4 arrangements), 2x2x1x1 (= 4 arrangements), and 2x2x1x1 (=4 arrangements). If we add these together, we get 16 different ways.


3) How many ways can these people be arranged if they must be positioned with people of the same sex next to each other? There are four configurations for seating, which are MMFF, FFMM, FMMF and MFFM. Using the same problem-solving strategy as above, we get a total of 16 different ways.


Many people instantly solved 1) and 2), and thought that the answer to 3) could be obtained by simply subtracting 2) from 1). This is wrong because both 2) and 3) share two configurations which satisfy the rules of each arrangement. Another tricky (counter-intuitive) issue is the notion that 16 ways plus 16 ways = 32 ways. Obviously 32 is greater than 24. But when we think about it, we realize that this is indeed sensible, because of the fact that 2) includes some of the same arrangements as in 3), so there will have to be an element of double-counting.
_____________________________________________________________
Our remaining problem from the previous day's quiz:

3. What is the probability that, if the first ball's color was not identified and eliminated from the game, that the next ball that you selected would blue?

Yep. A trick question. The answer would be the same as in question 1, above, because you are merely performing the same operation over again with the same number of balls. However...if you read the question thinking that a ball with an unidentified color was eliminated and not replaced, the answer is more complicated. It is what my math tutor used to call a "conditional probability problem". It poses a challenge.

If the eliminated ball were red, the number of blue remaining would be 30, with 19 red remaining; but if the eliminated ball were blue, the number of blue remaining would be 29, with 20 red left. In either case, the number of balls left over would be 49. What to do?

If a blue had been eliminated, the new probability of a blue being chosen would be 29/49 (.59); if a red had been eliminated, the new probability of blue being chosen would be 30/49 (.61). Either one of two things has occurred, and we do not know which...but we do know the likelihood (probability) of each one of these events. We know that the first one (a blue ball being chosen) was 30/50 (or .60), and that the second one (a red ball being chosen) was 20/50 (or .40).

The computation would be as follows (.60)x(.59) + (.40)x(.61) = .354 [the probability of a blue being chosen after a blue was eliminated from the group] + .244 [the probability of a blue being chosen after a red was eliminated from the group] = .598, or 59.8% . What we have done is to find the probabilities of each possibility (.60 and .40), and multiplied each by its resultant probability of blue being chosen. We added them together because we had to count both of possible ways in which we eliminated a ball from the group, i.e., by picking a blue one first, or by picking a red one first. (phew!)