## Monday, February 9, 2009

### BRAINTENANCE QUIZ 1/9/09

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Dear Friends:

Before we get started on our cerebration (which sounds rather like a Japanese word), I would like to share a letter which I received from a fellow Braintenance proponent:

Dear Douglas Castle:

Thanks for using our Quiz Stop widget "How Fast Do You Read?" on http://www.braintenance.blogspot.com/. We are thoroughly impressed by your insightful, entertaining list of educational resources on the Web.

Congratulations on your excellent research.

I would like to recommend another free, family-friendly resource for mental self-growth, of hopeful interest to your readers.

Mind Bluff (http://mindbluff.com/) offers free brain teasers, riddles, and mental illusions for all ages, recommended by PC World. Sample pages: Reaction Time Test (http://mindbluff.com/reaction.htm), Is Your Brain Cross-Lateralized? (http://mindbluff.com/phplater.htm), Necker Cube Illusion (http://mindbluff.com/necker.htm), and Knight's Tour Chess Problem (http://mindbluff.com/askchess.htm).

We would greatly appreciate a link from your Web site to any of our pages on Mind Bluff.

Kind Regards,

John DiPrete
http://www.mindbluff.com/

I will now be featuring John's Mindbluff site in a new set of links incorporated in MIND EXERCISE 2, above. Again, thank you, John.

Today's problem is a fairly straightforward one, with several parts:

1. How many cubic feet are contained in a box which is 3 feet by 3 feet by 5 feet?

2. In the above question, what is the answer in cubic yards?

3. In the above question, how many square feet of surface area are there on the container?

4. Would the container in the above question fit into a container which is 2 feet by 4 feet by 6 feet?

5. What would be the diameter of the largest ball (sphere) which could fit into the container described in 1), above?

Faithfully,

Douglas Castle
____________________________________________________________
Some hints toward answers to the last quiz follow for your review:

1) If you receive a solicitation from a charity (you're the first one), and the email has a directive that you send the message out to two friends, and they are each to do the same, and so forth, how many generations of mailing will it take (yours is the first, your two friends are the second, and so on) for a single mailing to go out to more than 1 million recipients? Everyone seems to receive chain letters. They work by a pricnciaple called geometric expansion. In this case, each phase of expansion is a power of 2. Your level is one, and you've sent out two messages. Your friends' level is two, and they've sent out 4 messages. Your friends' friends' level is three, and they've sent out 8 messages... The problem, restated, is, "TWO TO WHAT POWER EQUALS OR EXCEEDS ONE MILLION?"

2) Applying the same circumstances and parameters as in question 1, above, what would your answer be if each recipient were required to send a copy of the email to three friends, instead of two. The problem, restated, is , "THREE TO WHAT POWER EQUALS OR EXCEEDS ONE MILLION?"

3) If an executive consistently deposits 10% of her gross income into a special savings account, and her gross income grows at an average rate of 5% annually (her employer is a tightwad), how many years will it take before she accumulates (interest notwithstanding) one year's gross income (her first year's gross income) in the bank? There are two variables...salary is increasing at 5% per year, and our executive is saving 10% of that amount each year... The first year she saves (.10)(1.05). The second year she saves (.10)(1.05)(1.05). In each sucessive year, she will save the previous year's amount, multiplied by 1.05.

4) Why is it that when banks stop making loans to businesses, that the economy goes further into recession? If banks stop making loans to businesses, those businesses cannot buy equipment, property, inventory or create new jobs. Many businesses survive based upon credit.

5) Why is it that when banks stop making loans to consumers (principally through credit cards, auto loans and home mortgages), that the economy goes further into recession? This is simple. If people do not have credit available, they tend to hoard their funds and not spend -- this effect is worsened if they do not believe that credit will become available in the near future. Our economy (in the US, has been fueled by debt and anticipated additional credit for many years).