Know of any puzzles dealing with exponents?

[brum]

I'm currently doing a project for my Computer Science class (this is in QBASIC).

The purpose is to "teach" someone how to do something and include some type of game. For example, you could teach someone to Add/Subtract and give them clues and help them along the way.

So I've decided on teaching exponents. After first talking about what they are and how to do 'em, I then plan to make a game versus a computer opponent in which you race to finish the race first by doing lots of exponent problems and so if you get a problem right, you move a little bit closer to the finish.

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Finally, I would like to have a puzzle or 2 that deals with exponents. I'm trying to find some cool little tricks or a tricky problem that deals with exponents to have as the last part of my program. So if you guys can remember any cool or tricky problems that deal with exponents (no matter how complex) could you post them here please?

Or... if you know of a good website that has some good exponent problems that are difficult/fascinating -- that'd be great too.

--- Thanks in advance for the help, I'll be googling for ideas in the meantime. I thought about putting this into the "Homework Help" forum but I thought others might benefit from this thread if people post some cool stuff.

 

[Hurkyl]

I think some standard tricks would be to use situations that are the exceptions to the usual identities. For example:


( (-1)^2 )^(1/2) = 1

The rule (a^b)^c = a^(b*c) is only generally valid for a positive, so throwing in a few with negative bases would be good to remind the student of that fact.


Another cool trick is:

(a + b)^p = a^p + b^p (mod p)

When p is prime. That's probably beyond the scope of your program, though.

Hurkyl

 

[tacman]

One puzzle that deals with exponents is the "Exponent Tower" puzzle. This puzzle involves creating a tower of exponential expressions that all equal the same number. For example, you could start with the number 8 and create a tower like this:

8 = 2^3

2^3 = (2^2)^2

(2^2)^2 = (2^1)^4

(2^1)^4 = 1^4

1^4 = 1

The goal is to create the tallest tower possible using only exponential expressions with whole number exponents. This puzzle can be made more challenging by using larger numbers or including negative exponents.

Another puzzle involving exponents is the "Simplify the Expression" puzzle. In this puzzle, you are given a complex exponential expression and must simplify it to a single number. For example:

(2^3 * 2^2)^4 = 2^(3*4) * 2^(2*4) = 2^12 * 2^8 = 2^(12+8) = 2^20

Other variations of this puzzle could involve using negative exponents or fractional exponents.

As for websites, I recommend checking out Math Playground (https://www.mathplayground.com/exponents.html) and Math is Fun (https://www.mathsisfun.com/exponent.html) for more exponent puzzles and games. Good luck with your project!