Arrgh, me Hearties! Afore we commence, let's solve the last bunch of puzzles from the previous post:
Here are those several fine mind-twisters that kept your brain throbbing...
1. Any number, when divided by zero, equals what? Infinity, unless the number is zero.
2. What is the sum of all numbers from 1 to 1,000? 500,500. The shortcut formula for the sum of an arithmetic series is just N x (N+1)/ 2, or, in this case, 1000 x 1001 /2. Doing the math, our answer will come to 500,500.
3. What is the sum of all of the even numbers from 1 to 1,000? This is a tricky one. You know that the total number of numbers (sounds silly, eh?) will be 500, because the total series is comprised of half even numbers, and half odd ones, e.g., 500 of each. Logically, if you look at the 500 even numbers, you'll note that they are each a doubling of an odd number. For example, 2 is 1x2, 4 is 2x2, 6 is 3x2, 8 is 4x2...what we have is a really a series of the numbers of 1 through 500 twice. Going further, the sum of a 500 number arithmetic series is 500x501/2, or 125,250. Doubling this number gives us 250,500. Hence (nowthen), the sum of all of the even numbers from 1 to 1000 is 250,500.
4. What is the sum of all of the odd numbers from 1 to 1,000? Boy, we're smart. All we have to do is take the sum of the entire series (even and odd numbers consecutively ordered), which is 500,500, and reduce it by the sum of all of the even numbers, which we found in the previous problem. So...500,500 - 250,500 = 250,000.
5. What number, when divided by itself, equals itself? Every number, when divided by itself, will equal 1.
6. What number, when multiplied by itself, equals 729? The square root of 729, is can be found by a mathematically complex formula which involves an iterative process -- or you can use your pocket calculator to get 27.
7. What three-digit number, whose digits are added together equals the same as the product when its digits are multiplied by eachother? The number 123. Or 231. Or 321. Or 312. Or 213. Or 132.
8. How many correct answers can there be to the previous question? Six.
9. Why does it seem that time passes more quickly as we grow older? Because as we get older, each additional year becomes a decreasing fraction of our entire life as lived so far. For example, a three-year-old's last year represents 33.33% of his entire lifetime, while a sixty-year-old's last (most recent) year represents a mere 1.67% of his entire lifetime.
10. How far can a dog run into the woods? Halfway, and then he is running out.
11. What are these two words: One is an amusing story, and the other is a cure for a poison. They are ANECDOTE and ANTIDOTE.
12. What do we run into after we've run out? You'll have to figure this one out for yourself. Drop me a line. Let me know what you think the answer is.
13. What is the term for those interesting shapes and patterns we see when we close our eyelids? Phosphenes.
14. How many moons are there during a period of three months? Actually, only one. The same one every night for three months. It may look different, but it is Earth's one and only known moon.
15. What question will never be answered? The one which is never asked.
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And now, for some new mind-wringers:
1. How many ways can you arrange four blocks in a vertical column?
2. What portion of the human brain is thought to be the oldest (the most primitive)?
3. How many letter "i" s are in the two-word expression, "eyes only"?
4. What is the literal translation of the word DINOSAUR?
5. How many different combinations of American coins can be added together which will equal thirty one cents?
6. What is wrong with the expression, "You can't have your cake and eat it too." ?
7. What is wrong with the expression, "He's adding insult to injury." ?
8. What is wrong with the expression, "Birds of a feather flock together." ?
9. What is the official language of the United Nations?
10. What is the English translation of the latin expression "NOVUS ORDO SECLORUM"? This expression is on every $1 bill.
11. What is the difference in meaning between the words SCRIPT and SCRIP?
12. What is the difference in meaning between the words ASSENT and ASCENT?
13. Assuming that nothing else is changed, if your arteries and veins were wider, would your blood pressure go up or down? Why.
Faithfully,
Douglas Castle
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