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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
2 years ago

No vote yet
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Please post your final answers here. Raj Magesh · 2 years ago

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@Raj Magesh the triplets should not be a negative number , should be increasing order and the numbers should not repeat Angela Fajardo · 2 years ago

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@Angela Fajardo 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. Angela Fajardo · 2 years ago

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@Angela Fajardo Excellent, great job! You win! My phrasing was: three distinct, positive real numbers arranged in increasing order. Raj Magesh · 2 years ago

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@Raj Magesh there should be no negative number?? Angela Fajardo · 2 years ago

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@Angela Fajardo Is that the only rule? Raj Magesh · 2 years ago

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@Raj Magesh nope , the numbers should be increasing too. Angela Fajardo · 2 years ago

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@Angela Fajardo Great job, you're almost there. One more condition is left. Check the triplets you posted once more. Raj Magesh · 2 years ago

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@Raj Magesh should be not a fraction??? Angela Fajardo · 2 years ago

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@Angela Fajardo Nope. Hint: (1,2,2) was not valid. Raj Magesh · 2 years ago

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@Raj Magesh On this occasion of the new year I declare the all of your triplets follow Pythagoras theorem! Sarthak Tanwani · 2 years ago

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@Sarthak Tanwani Nope.(13,16,19),(1,2,3) also follow the rule but aren't Pythagorean triplets Snehdeep Arora · 2 years ago

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@Raj Magesh The triplet follows the Pythagoras theorem Maitri Mishra · 2 years ago

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@Raj Magesh The triplets must be in increasing order Alita Toh · 2 years ago

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@Alita Toh Close. Two more aspects remain. Can you figure those out? How would you go about it? Raj Magesh · 2 years ago

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@Raj Magesh For a triplet (a,b,c),a^2 plus b^2 equals c^2.Lengths of right triangle. Abdur Rehman Zahid · 2 years ago

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@Raj Magesh 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 :) Zi Song Yeoh · 2 years ago

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@Zi Song Yeoh Still nope. Did you check out all the triplets others posted? Raj Magesh · 2 years ago

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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... Ivan Koswara · 2 years ago

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0.36 , 0.4 , 0.534345 Angela Fajardo · 2 years ago

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@Angela Fajardo Yes. Raj Magesh · 2 years ago

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

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@Angela Fajardo No. Raj Magesh · 2 years ago

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  • 1 , -2 , -3
Angela Fajardo · 2 years ago

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@Angela Fajardo No. Raj Magesh · 2 years ago

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111 , 222 , 333 Angela Fajardo · 2 years ago

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@Angela Fajardo Yes. Raj Magesh · 2 years ago

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5 , 43 , 97 Angela Fajardo · 2 years ago

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@Angela Fajardo Yes Raj Magesh · 2 years ago

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44 , 88 , 122 Angela Fajardo · 2 years ago

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@Angela Fajardo Yes. Raj Magesh · 2 years ago

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@Raj Magesh 0.5, 0.6, 0.7 Snehdeep Arora · 2 years ago

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@Snehdeep Arora Yes. Raj Magesh · 2 years ago

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10 , 100 , 1000 Angela Fajardo · 2 years ago

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@Angela Fajardo Yes. Raj Magesh · 2 years ago

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101 , 102 , 103 Angela Fajardo · 2 years ago

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@Angela Fajardo Yes. Raj Magesh · 2 years ago

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1 , 3 , 7 Angela Fajardo · 2 years ago

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@Angela Fajardo Yes. Raj Magesh · 2 years ago

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1 , 2 ,2 Angela Fajardo · 2 years ago

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@Angela Fajardo No. Raj Magesh · 2 years ago

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Comment deleted Jan 01, 2015

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@Angela Fajardo Yes. Raj Magesh · 2 years ago

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2 , 1 , 3 Angela Fajardo · 2 years ago

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@Angela Fajardo No. Raj Magesh · 2 years ago

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

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@Yash Singhal Yes. Raj Magesh · 2 years ago

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17,19,11 Alita Toh · 2 years ago

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@Alita Toh No. Raj Magesh · 2 years ago

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@Raj Magesh 13,16,19 Snehdeep Arora · 2 years ago

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@Snehdeep Arora Yes. Raj Magesh · 2 years ago

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@Raj Magesh Does any 3 consecutive terms of any arithmetic progression follow? ( in addition to Pythagorean triples) Snehdeep Arora · 2 years ago

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@Snehdeep Arora 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 Raj Magesh · 2 years ago

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29,21,20 Alita Toh · 2 years ago

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@Alita Toh No. Raj Magesh · 2 years ago

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(1 , 2 ,3) Carl Johnson · 2 years ago

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@Carl Johnson Yes. Raj Magesh · 2 years ago

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12 , 14 , 16 Carl Johnson · 2 years ago

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@Carl Johnson Yes. Raj Magesh · 2 years ago

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

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@Abdur Rehman Zahid Yes. Raj Magesh · 2 years ago

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3,4,5?? Sarthak Tanwani · 2 years ago

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@Sarthak Tanwani Yes. Raj Magesh · 2 years ago

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@Raj Magesh I know it! Sarthak Tanwani · 2 years ago

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@Sarthak Tanwani Well, if you're certain your answer is right, post it above, as a reply to my comment. Raj Magesh · 2 years ago

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

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@Abdur Rehman Zahid Yes. Raj Magesh · 2 years ago

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

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@Mahdi Al-kawaz Well, I did mention that this rule applies only to nomzero reals, so this triplet is undefined. Raj Magesh · 2 years ago

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

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@Mahdi Al-kawaz No. Raj Magesh · 2 years ago

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Confirmation bias. Mursalin Habib · 2 years ago

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@Mursalin Habib By posting that comment, aren't you guilty of it? Calvin Lin Staff · 2 years ago

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@Mursalin Habib Shhh... Raj Magesh · 2 years ago

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5,12,13 Maitri Mishra · 2 years ago

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@Maitri Mishra Yes. Raj Magesh · 2 years ago

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

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@Tytan Le Nguyen Yes. Raj Magesh · 2 years ago

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@Raj Magesh 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. Tytan Le Nguyen · 2 years ago

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@Tytan Le Nguyen Great, but stay tuned, you might just be wrong! ;) Cheers! Raj Magesh · 2 years ago

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@Raj Magesh 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? Tytan Le Nguyen · 2 years ago

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@Tytan Le Nguyen Yes. :) Raj Magesh · 2 years ago

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

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@Byungjun Kim Yes, and I'll be discussing it later. :D Raj Magesh · 2 years ago

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