Hey Whyvillians! It's Deriko reporting to you, after quite some time now, about one of the most interesting subjects we all know and love. Ok, well maybe love is an exaggeration! But mathematics can turn out to be one of the most rewarding subjects as far as self-esteem goes. So instead of giving you a few excercises (like: what's 394 + 273??), I'm going to show you a completely different side to mathematics which has problems that take a bit of time and ingenuity (that's a noun, similar to ingenious, meaning smartness!).

Now before you go ahead and read the solutions, take some time to try and work out each question to yourself. I guarantee you that the satisfaction you will receive from solving, or even attempting, these questions is well worth the time and effort it would take to solve any one of them. So here we go: with solutions to follow!

First Problem:
One bacterium is placed in a glass. One second later, the bacterium divides in two. The next second, each of those bacteria divide in two again. This keeps happening. After one minute the glass is full. After how long was the glass half full?
Word Bank:
Bacterium - Singular for the word bacteria

Second Problem:
Jack tore out several successive pages from a book. The number of the first page he tore out was 183. The number of the last page he tore out has the same digits, but in a different order. How many pages did Jack tear out of the book?
Word Bank:
Successive - in a row
Digits - the smallers numbers that make up a number! e.g. the digits of 693 are six, nine, and three!

Third Problem:
A babysitter is minding three girls at her house, and the only information the mother has left for her about the children's ages was left on this note:
"I have three daughters, their ages are whole numbers, and the product of their ages is 36. I'd tell you the sum of their ages, but you'd still be stumped. My oldest daughter Annie likes to stay up late." The babysitter now had enough information to figure out the ages of the children.
How old were the three girls?
Word Bank:
Whole Numbers - 1, 2, 3, 4, 5, etc. It means no fractions or decimals!
Product - the result when you multiply things together
Sum - the result when you add things together

The third was is a bit more challenging than the others but each one of them is pretty nifty! Get a pencil and paper and give them all a shot, and even if you make a little progress, you'll still feel pretty good! The solutions are listed here below, so only read them if you're sure that you can't go on any further. Even a good mathematician knows their limits, right?

First Solution:
59 seconds! Here's why:
If the bacteria double after a second, then that means one second ago there were half as many bacteria! If the glass was full after a minute then at 59 seconds the glass is half full.

Second Solution:
136 pages! Check this out:
If the first page is odd, then the last page must be an even number! Because you have to rip out 2 pages at a time (front and back). So the last number is an 8. So the number of the last page he ripped out was 318! Because he ripped pages successively (in a row, counting up). So if we subtract these two... 318 - 182 = 136! (notice we subtract off 182 because if we subtracted off up to page 183, we'd be taking off page 183! we don't want to do that! Give yourself a pat on the back if you got 135 though.)

Third Solution:
The daughters are aged two, two, and nine! Try and follow this! The product of the ages is 36. And there are only 8 sets of 3 numbers that have a product of 36! Here they are: (1, 1, 36) (1, 2, 18) (1, 3, 12) (1, 4, 9) (1, 6, 6) (2, 2, 9) (2, 3, 6) (3, 3, 4) That's what the first piece of information tells us! The daughters have to be one of those 8 groups. Let's look at the sum of all the possible ages: 38, 21, 16, 14, 13, 13, 11, 10 (in order) Only two of them are the same! So that's why the mother said telling us the sum of the ages wouldn't help! So their ages are either: (1, 6, 6) or (2, 2, 9). The third piece of information solves this! We know she has an oldest daughter! So the children can't be (1, 6, 6) because then there would be 2 older daughters! Now we're done. The ages of the daughters, we've found are: two, two, and nine!

These questions are all designed to show you what real mathematics can be about! As you see, the more interesting the problem, the tougher the solution. But the more problems you do, the better you become! So kudos to anyone who solved even one of those questions. Keep an eye out for interesting mathematical challenges. They can be in the paper, in magazines, (rarely in textbooks!), and even on the Internet. If you're in highschool in America, the American High School Math Exam is packed full of questions like these.

The point is to keep your mind open. Solving, or attempting, questions like these is good exercise for your mind. Some of you may have a low frustration point (if you gave up too soon, or if you just looked to the answers), so doing more of these types of questions allows you to just sit down and do something for longer. Try to concentrate on what's going on around you.

I'd like some feedback on these questions. If you tried them, if you solved them, or if you just found them interesting. I might even get some more problems, without solutions, and offer prizes! What do you think? Can't wait to hear from you!

A faithful soldier of The Whyville Way,
Deriko