Math game...

[Sparkey]

My pre-calculus instructor last quarter enjoyed teaching about functions by playing what he called his game. He spoke of inputs, rules and outputs, saying, "I'll give you two and you give me the third."

We would spend a lot of time with sequences, for instance he might present "2, 4, 8, 16, 32" for outputs and we could guess he was talking about the powers of 2 (exponents) and etc. Of course his game was more difficult than this example -- like the Fibonacci series or other things that people with their master in math like but this isn't that bad.

Here then is a derivative on the "game". I will give three outputs (a sequence) and then somebody can guess a number and I'll answer saying, "True" if the next number follows my rule or "False" if it does not.

Here's the first set of 3:
(1, 4, 6)

Now your part is to make a guess about what number or numbers might come next. Together we will build up a set of numbers that follow the rule. The purpose of the guessing is to discover the rule that I'm using. Sounds easy, doesn't it?

 

[reba]

7

 

[Sparkey]

Seven (7) follows the rule so it is "True"

Do you have a guess for the rule or would you like to try another number first?

 

[reba]

did you change numbers?

 

[Sparkey]

Your first post came very fast (sorry) but I did follow the rule; the numbers are "fixed". Neither they nor the rule I follow will change from now on.

(I was trying to be 'tricky' at first but thought it better to keep it simple to start)

 

[reba]

ok i doubt i willever get another one right

 

[Sparkey]

Here's the first set of 3:
(1, 4, 6)

First guess: 7
The guess is 'true' and follows the rule.

 

[TOG]

1,4,6,7...

And the next number is 7 again, and the rule is +3, +2, +1, +0.

The TOG​

 

[Sparkey]

The next number is NOT 7 because it does not follow the rule.

Good guess though. I like the way you are thinking.

 

[Sparkey]

We can change the way this works too (later) if it lasts a day with nobody guessing the rule so that the guesses could be another set of 3 numbers instead of just 1. My reply would be the same, either 'true' the set follows the rule, or 'false' it does not. I'm not trying to make it impossible. Somebody is going to figure it out.

I'd like to keep it this way for a bit so others can play too.

 

[Claudya]

Next in the sequence is 10?

 

[for_his_glory]

12
take from the seven as 1+3+2= 12

 

[Sparkey]

Next in the sequence is 10?

Your guess, "10" is True because it follows the rule.

Do you have a guess for the rule we are using or would you like to try another number first?

 

[Sparkey]

12
take from the seven as 1+3+2= 12

Your guess, "12" is TRUE because it follows the rule.

I'm not sure I understand the rule you used but if you'd like to explain it further I can confirm. No, wait. The rule is NOT: 1+3+2 = 12.
At this point there are probably hundreds of "rules" that could be used. The guesses so far have all be excellent but just not the right one (yet).

So far, our entire set of (1,4,7,10,12) follows the rule. Hope this helps!

 

[Claudya]

So far, our entire set of (1,4,7,10,12) follows the rule. Hope this helps!

There used to be a 6, too. ;-)

Anyway, next after 12 is 13, right?

 

[TOG]

What we have is...
1-4-6-7-10-

Would the next three number be...
12-13-16?

The TOG​

 

[jay55]

7

Hey Reba, not so fast, give the rest of us a chance!

 

[reba]

If i can figure it out any one can...

 

[jasonc]

ah post a function or quadratic and find the first deritive. that would be fun to do again.

 

[jay55]

If i can figure it out any one can...

Didn't I see you giving a lecture on differential equations at the Oxford School of Mathematics in the 80's? Unfair advantage!