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**

- 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. - Your objective is to
**guess that rule correctly**. - To begin with, I will give you a
**single triplet of numbers**that fits the rule. - 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". - 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!

## Comments

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TopNewestPlease post your final answers here. – Raj Magesh · 2 years, 2 months ago

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– Angela Fajardo · 2 years, 2 months ago

the triplets should not be a negative number , should be increasing order and the numbers should not repeatLog in to reply

– Angela Fajardo · 2 years, 2 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.Log in to reply

– Raj Magesh · 2 years, 2 months ago

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

– Angela Fajardo · 2 years, 2 months ago

there should be no negative number??Log in to reply

– Raj Magesh · 2 years, 2 months ago

Is that the only rule?Log in to reply

– Angela Fajardo · 2 years, 2 months ago

nope , the numbers should be increasing too.Log in to reply

– Raj Magesh · 2 years, 2 months ago

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

– Angela Fajardo · 2 years, 2 months ago

should be not a fraction???Log in to reply

– Raj Magesh · 2 years, 2 months ago

Nope. Hint: (1,2,2) was not valid.Log in to reply

– Sarthak Tanwani · 2 years, 2 months ago

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

– Snehdeep Arora · 2 years, 2 months ago

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

– Maitri Mishra · 2 years, 2 months ago

The triplet follows the Pythagoras theoremLog in to reply

– Alita Toh · 2 years, 2 months ago

The triplets must be in increasing orderLog in to reply

– Raj Magesh · 2 years, 2 months ago

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

– Abdur Rehman Zahid · 2 years, 2 months ago

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

– Zi Song Yeoh · 2 years, 2 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 :)Log in to reply

– Raj Magesh · 2 years, 2 months ago

Still nope. Did you check out all the triplets others posted?Log in to reply

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

I wonder if a game of Zendo will attract people... – Ivan Koswara · 2 years, 2 months ago

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0.36 , 0.4 , 0.534345 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

-5 , - 4 , -1 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

No.Log in to reply

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– Raj Magesh · 2 years, 2 months ago

No.Log in to reply

111 , 222 , 333 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

5 , 43 , 97 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

YesLog in to reply

44 , 88 , 122 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

– Snehdeep Arora · 2 years, 2 months ago

0.5, 0.6, 0.7Log in to reply

– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

10 , 100 , 1000 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

101 , 102 , 103 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

1 , 3 , 7 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

1 , 2 ,2 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

No.Log in to reply

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

2 , 1 , 3 – Angela Fajardo · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

No.Log in to reply

\(\huge{9,40,41}\). – Yash Singhal · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

17,19,11 – Alita Toh · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

No.Log in to reply

– Snehdeep Arora · 2 years, 2 months ago

13,16,19Log in to reply

– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

– Snehdeep Arora · 2 years, 2 months ago

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

– Raj Magesh · 2 years, 2 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. :DLog in to reply

29,21,20 – Alita Toh · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

No.Log in to reply

(1 , 2 ,3) – Carl Johnson · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

12 , 14 , 16 – Carl Johnson · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

1,sqrt(phi),phi – Abdur Rehman Zahid · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

3,4,5?? – Sarthak Tanwani · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

– Sarthak Tanwani · 2 years, 2 months ago

I know it!Log in to reply

– Raj Magesh · 2 years, 2 months ago

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

Would the triplet (12,35,37) fit by any chance? – Abdur Rehman Zahid · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

\(\Large{0,10,20}\) – Mahdi Al-kawaz · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

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

\(\Large {10,20,10}\) – Mahdi Al-kawaz · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

No.Log in to reply

Confirmation bias. – Mursalin Habib · 2 years, 2 months ago

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– Calvin Lin Staff · 2 years, 2 months ago

By posting that comment, aren't you guilty of it?Log in to reply

– Raj Magesh · 2 years, 2 months ago

Shhh...Log in to reply

5,12,13 – Maitri Mishra · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

Would the triplet 15, 20, 25 fit by any chance? – Tytan Le Nguyen · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes.Log in to reply

– Tytan Le Nguyen · 2 years, 2 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.Log in to reply

– Raj Magesh · 2 years, 2 months ago

Great, but stay tuned, you might just be wrong! ;) Cheers!Log in to reply

– Tytan Le Nguyen · 2 years, 2 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?Log in to reply

– Raj Magesh · 2 years, 2 months ago

Yes. :)Log in to reply

Might this have anything to do with the Veritasium Youtube video? – Byungjun Kim · 2 years, 2 months ago

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– Raj Magesh · 2 years, 2 months ago

Yes, and I'll be discussing it later. :DLog in to reply