# Guess the Rule ~ An Interactive Game!

Hey Guys!

This is an interactive "game" of sorts, where you are the participants.

To those of you who already know about this game, please don't spoil it for the rest by commenting on this post. You're welcome to join in on the discussion of the game after it's over. And now, let's begin!

The Rules of the Game

1. I have a mathematical rule in mind, which applies to ordered triplets of non-zero real numbers. Some triplets of numbers fit that rule, other triplets of numbers do not.
2. Your objective is to guess that rule correctly.
3. To begin with, I will give you a single triplet of numbers that fits the rule.
4. You are allowed to give me some triplets of numbers by posting each triplet as a separate comment, and I will tell you whether or not your triplet satisfies the rule by replying "Yes" or "No".
5. Once you are certain what the rule is, post it as a reply to my comment "Please post your final answers here."

After the game ends (that is, when the first correct answer is posted), the discussion of this game and its implications will be posted as a new note, which I will link to here.

The first person to guess the rule correctly wins a solid-gold virtual trophy, followed by a tray of freshly-baked virtual cookies and a glass of virtual milk. But seriously, you might just learn something from this, so join in!

The first triplet which satisfies my rule is:

$\Huge 6,8,10$

Update 1

Well, many people have commented, some nearing very close to the answer. Remember, the rule may not be a simple rule. It can include several different aspects, and you have to discover all of them. For example, I've given you one part of it already, that only real numbers can be part of the triplet. I also told you that they have to be non-zero. So, with this information, your starting rule should be something like, "A triplet of non-zero real numbers."

There are other aspects to the rule, some of which you have guessed correctly. Two more aspects remain. Who will figure those final aspects out? And don't worry, though the rule is somewhat arbitrary, it's not as arbitrary as "The sum of the three numbers should not be 42." Cheers!

Update 2 The game is now officially over. Angela Fajardo won the competition!

Note by Raj Magesh
4 years, 8 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

- 4 years, 8 months ago

the triplets should not be a negative number , should be increasing order and the numbers should not repeat

- 4 years, 8 months ago

Excellent, great job! You win! My phrasing was: three distinct, positive real numbers arranged in increasing order.

- 4 years, 8 months ago

A triplet of non-zero real numbers should be in an increasing order , not have a negative number , and don't have a repeating number.

- 4 years, 8 months ago

For a triplet (a,b,c),a^2 plus b^2 equals c^2.Lengths of right triangle.

- 4 years, 8 months ago

The triplets must be in increasing order

- 4 years, 8 months ago

Close. Two more aspects remain. Can you figure those out? How would you go about it?

- 4 years, 8 months ago

The triplet follows the Pythagoras theorem

- 4 years, 8 months ago

On this occasion of the new year I declare the all of your triplets follow Pythagoras theorem!

- 4 years, 8 months ago

Nope.(13,16,19),(1,2,3) also follow the rule but aren't Pythagorean triplets

- 4 years, 8 months ago

there should be no negative number??

- 4 years, 8 months ago

Is that the only rule?

- 4 years, 8 months ago

nope , the numbers should be increasing too.

- 4 years, 8 months ago

Great job, you're almost there. One more condition is left. Check the triplets you posted once more.

- 4 years, 8 months ago

should be not a fraction???

- 4 years, 8 months ago

Nope. Hint: (1,2,2) was not valid.

- 4 years, 8 months ago

real numbers $a, b, c$ such that $a \le b \le c$ and $a^2 + b^2 = c^2$. Note that a right triangle can't have negative length :)

- 4 years, 8 months ago

Still nope. Did you check out all the triplets others posted?

- 4 years, 8 months ago

Would the triplet 15, 20, 25 fit by any chance?

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

Okay, thank you. I'm probably know what the rule is, but just to make the game longer and for others to have fun, I'll probably just sit this one out until the game ends.

- 4 years, 8 months ago

Great, but stay tuned, you might just be wrong! ;) Cheers!

- 4 years, 8 months ago

Oh, one more question just to be sure. Would any of the triplets (8, 15, 17) and (20, 21, 29) fit this type of triplet?

- 4 years, 8 months ago

Yes. :)

- 4 years, 8 months ago

5,12,13

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

Confirmation bias.

- 4 years, 8 months ago

By posting that comment, aren't you guilty of it?

Staff - 4 years, 8 months ago

Shhh...

- 4 years, 8 months ago

$\Large {10,20,10}$

- 4 years, 8 months ago

No.

- 4 years, 8 months ago

$\Large{0,10,20}$

- 4 years, 8 months ago

Well, I did mention that this rule applies only to nomzero reals, so this triplet is undefined.

- 4 years, 8 months ago

Would the triplet (12,35,37) fit by any chance?

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

3,4,5??

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

I know it!

- 4 years, 8 months ago

Well, if you're certain your answer is right, post it above, as a reply to my comment.

- 4 years, 8 months ago

1,sqrt(phi),phi

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

12 , 14 , 16

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

(1 , 2 ,3)

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

29,21,20

- 4 years, 8 months ago

No.

- 4 years, 8 months ago

17,19,11

- 4 years, 8 months ago

No.

- 4 years, 8 months ago

13,16,19

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

Does any 3 consecutive terms of any arithmetic progression follow? ( in addition to Pythagorean triples)

- 4 years, 8 months ago

If that's your final answer, post it above as a reply to my comment. I suppose I'll reveal the answer in a few hours. :D

- 4 years, 8 months ago

$\huge{9,40,41}$.

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

2 , 1 , 3

- 4 years, 8 months ago

No.

- 4 years, 8 months ago

1 , 2 ,2

- 4 years, 8 months ago

No.

- 4 years, 8 months ago

1 , 3 , 7

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

101 , 102 , 103

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

10 , 100 , 1000

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

44 , 88 , 122

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

0.5, 0.6, 0.7

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

5 , 43 , 97

- 4 years, 8 months ago

Yes

- 4 years, 8 months ago

111 , 222 , 333

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

• 1 , -2 , -3

- 4 years, 8 months ago

No.

- 4 years, 8 months ago

-5 , - 4 , -1

- 4 years, 8 months ago

No.

- 4 years, 8 months ago

0.36 , 0.4 , 0.534345

- 4 years, 8 months ago

Yes.

- 4 years, 8 months ago

Note that this game is very similar to Zendo in its core.

I wonder if a game of Zendo will attract people...

- 4 years, 8 months ago

Might this have anything to do with the Veritasium Youtube video?

- 4 years, 8 months ago

Yes, and I'll be discussing it later. :D

- 4 years, 8 months ago