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Math game...

For those who don't want to look back at the first post:

:bump

Sparrowhawke said:
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?
Click to expand...

All of the suggestions (guesses) supplied so far are "True". They all follow my rule. Maybe I should have made this tougher?

It's getting close to the time where I should formally allow sets of three numbers.
The way that will work is similar to how it's been going where a respondent supplies the numbers and I'll reply with "True," meaning "yes, those numbers do follow the rule or "False" meaning that the numbers supplied do not follow the rule.

That could speed up the answers and certainly will give more information.

For instance, if you like you could reply with:
(19, 31, 127)
and I would evaluate your 3 number set. :chin (shhhh... this one is also "True" but since nobody asked, don't tell)
:coke
 
So, we have...

1-4-6-7-10-12-13-16

I would have thought 18 came next, but if it's 17, then I obviously have the wrong rule. I'll have to think about it some more.

The TOG​
 
I may have lead you down the wrong track a little - not intentionally because my intent was to evaluate a single guess at a time. Technically we have the given three numbers (1, 4, 6) and a true response to the next several guesses, including reba's guess of 7. It just so happens that the entire sequence of guesses (when taken together) also comply. But I've never played this on a forum before, it's only been one-on-one. By the way, I stumped my professor with it and he acted like he wasn't amused but i could tell he couldn't wait to try it on one of his cronies.

If we were playing one-on-one we'd have something more like
GIVEN: (1, 4, 6)
Reply 1: (1, 4, 6, 7)? -- my response: True
Reply 2: (10)? -- my response: True
Reply 3: (12)? -- my response: True
Reply 4: (13)? - my response: True
Reple 5: (16)? -- my response: True
Reply 6: (17)? -- my response: True

With additional information: (1, 4, 6, 7, 10, 12, 13, 16, 17) -- also True
Careful readers will note that (19, 31, 127) also evaluates as True because that particular set of three also complies. But I threw that in more as a Red Herring than anything else.

Hope this helps. By the way, when my son first shared this math game with me I was stumped. It was very frustrating. More than once I thought I had it cold but then... no.
 
Last edited:
Hey sparrow didn't you already tell us this "rule" a while ago in another post or am I imagining it ?

1, 4, 6, 7, 10, 12, 13, 16, 17 may I add 21, 27,39, 41, 67, 83 ?
 
TOG said:
So, we have...

1-4-6-7-10-12-13-16

I would have thought 18 came next, but if it's 17, then I obviously have the wrong rule. I'll have to think about it some more.

The TOG​
Click to expand...

Me too. I would have thought it's 18.
Booooo!! :grumpy
 
agua. said:
Hey sparrow didn't you already tell us this "rule" a while ago in another post or am I imagining it ?

1, 4, 6, 7, 10, 12, 13, 16, 17 may I add 21, 27,39, 41, 67, 83 ?
Click to expand...
It wasn't me and your numbers are more than three.
 
The guessing method can change now. If your reply lists 3 numbers I will evaluate and let you know if they follow the rule or not.

The first set is:

(3, 5, 14) = .True.

So if you reply with a single number, your number will be added as the fourth element of my set.
If the reply is a set of three numbers it will be evaluated independently. You may trust that I will not lie about it.

Also, if anybody simply must know the rule -- send a private message and I'll share the 'secret'.
Well, anybody but agua, that is! *wink* :wave
 
TOG said:
In the first post, you said



I'm confused. Could you please tell us what the entire series that has been guessed so far is?

The TOG​
Click to expand...
TOG,

Sorry. It's my fault because I started giving more information than was absolutely needed. When I was first exposed to this - my son presented it as a math function and a sequence problem -- but really? That's too narrow of a view. I still think in this manner. But the way we played (and I never did guess the correct rule - I had to give up so he would tell me) was that he would give 3 numbers and I'd guess the 4th. So what happened here is I gave the first 3 numbers and reba guessed the 4th. But then you made a very intuitive leap and guessed the 5th element and the rule.

When I played with my son I was able to make a guess at the rule at any time. So even though your thought about the 5th number was incorrect I wanted to reply to your query about the rule. In the meantime (because I was AFK -- at school) there were several other guesses and when they were evaluated they were all true in that my rule COULD be used to arrive at their guesses too.

So I should have stopped and tried to explain (as I did subsequently) that I was evaluating for each individual guess. That's what I was doing when I started the whole "(1, 4, 6) and (7)? == .True" reply, repeating it to show my method for each guess. But I also noticed that coincidentally all of the guesses, when taken in order and as a whole, would follow my rule. I was quite surprised by this.

So now we come to a place where I will NOT change the original rule but have given another set of three numbers that follow the same rule.
(3, 5, 14) = .True.
Also, you may reply with a single number and I will respond as if it is the fourth element of my set --OR-- you may respond with another set of three numbers and I'll just check your numbers without adding them to my original set. If your three numbers follow the rule then you get the .TRUE. response. If your single number, when added to my set of three, follows the rule, you get the .TRUE. response as well.

You're also free to check all the previous answers to come up with your own suppositions -- but the main way of discovery should revert back to the way I was introduced to it by my son.

Hope this helps! Feel free to PM me if you want. I'm glad you're enjoying the puzzle - I like them very much too.
 
I think I understand now. Are you saying that 1-4-6 and 3-5-14 both follow the same rule, but have different starting points, sort of like 1-2-4 and 3-6-12 both follow the rule of always doubling the previous number, but they have different stating points and are not part of the same series?

The TOG​
 
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