## Sunday, August 30, 2009

### SOLUTIONS (and more problems, of course)

Dear Friends:

Firstly, here are the answers to "Get On The Brain Train" from several days ago:

1. How much better (in terms of a percentage) than the original is a new model which costs half the price and does the job in half the time?

A: If the new model costs half the price, it is also twice (2 times) as inexpensive; and, if the new gadget does the job in half the time, it is also twice (2 times) as powerful as the old one. The new gadget is 2 x 2 times as efficient as the old one, which means that it is 4 times as effective (400%) as the old one. Since the new one is operating at 400%, and the old one was operating (setting the standard of measurement) at 100%, the new gadget is 300% better. Remember: The answer is not 4 times better, or 400%, because the question asks for the difference. Mrs. Scenendorf, my third-grade teacher, said that "difference means subtract." Not well stated, but I understood.
2. How much better (in terms of a percentage) than the original is a new version that does three times as much work at one-fourth the price?

A: As in the question above, 3 x 4 = 12 (or 1,200%). Subtracting 100% (by the Schenendorf Principle) gives us 1,100% better.

3. If Juan has only 80% of the IQ of his elder brother, Pincus (both children are the products of either an adoption or a mixed marriage), but Juan always earns 50% more than his brother, how much more efficient (in terms of a percentage) is Juan?

A: Juan is 80% as bright as his brother (or expressed in another way, he must think 100%/80% or 125% harder than his brother), but he earns 150% of what his brother earns (something must be said here about the virtues of ambition and hard work). Juan does more with less...first, we do the multiplication: 1.25 x 1.5 = 1.875. Juan is 187.5% as efficient as Pincus. But to answer the question as it was asked (and using the Schenendorf Principle), Juan is 87.5% more efficient.

4. If you take three steps forward and one step back, how long (in total steps forward) will it take for you to advance by fifty steps? Is there a formula for solving this type of problem?

A: Take 3 steps forward in order to advance 2 steps, then you must actually take 6 steps forward in total) in order to advance 4 steps, and 9 steps forward in order to advance 6 steps, and 12 steps forward to advance 8 steps ...Do you detect a pattern? Let's give your mind an additional day or two to identify the pattern, and to come up with the answer without actually pacing around in your house to do it empirically.

5. If your anticipated lifespan is 80 years, and you spend an average of 8 hrs per day sleeping, for how many years of your life will you have been awake?

A: Each day lasts for 24 hours (although sometimes it seems much longer, or much shorter -- but that is perception, and not measurement), so if you sleep 8 hours, you spend 8/24 or 33.33% of your day sleeping. If you continue to do this for 80 years, you'll have sleeping for 33.33% of 80 years, or 26.66 years sleeping. Applying the Schenendorf Principle, 80 total years minus 26.66 years sleeping leaves 53.33 years awake.

See you soon. Or as they used to say in the cult TV series, THE PRISONER, "BCNU."

Faithfully,

Douglas Castle