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!

No vote yet

1 vote

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## Comments

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TopNewestPlease post your final answers here.

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

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

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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.

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

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The triplets must be in increasing order

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

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The triplet follows the Pythagoras theorem

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

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

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there should be no negative number??

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Is that the only rule?

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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 :)

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

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

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Yes.

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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.

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5,12,13

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Yes.

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Confirmation bias.

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

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Shhh...

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\(\Large {10,20,10}\)

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No.

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\(\Large{0,10,20}\)

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

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

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Yes.

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3,4,5??

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Yes.

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I know it!

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1,sqrt(phi),phi

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Yes.

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12 , 14 , 16

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Yes.

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(1 , 2 ,3)

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Yes.

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29,21,20

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No.

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17,19,11

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No.

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13,16,19

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\(\huge{9,40,41}\).

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Yes.

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2 , 1 , 3

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No.

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1 , 2 ,2

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No.

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1 , 3 , 7

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Yes.

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101 , 102 , 103

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Yes.

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10 , 100 , 1000

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Yes.

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44 , 88 , 122

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Yes.

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0.5, 0.6, 0.7

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5 , 43 , 97

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Yes

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111 , 222 , 333

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Yes.

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No.

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-5 , - 4 , -1

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No.

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0.36 , 0.4 , 0.534345

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Yes.

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

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

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

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

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