# Is the answer to this math puzzle legit? **URL:** \ **Category:** The Game Room\ **Created:** [September 19, 2015, 2:49pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768 "2015-09-19T14:49:26Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 19, 2015, 2:49pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/1 "2015-09-19T14:49:26Z")
I was taking an online math puzzle. One of the questions was this: > [@](#): > > If 1=5 > 2=25 > 3=325 > 4=4325 > 5=??? The answer I gave was:[spoiler]54325. I figured the puzzle was recognizing that this was a pattern rather than a mathematical operation. Like the puzzle of listing a series of numbers in alphabetical order.[/spoiler] But the “correct” answer was:[spoiler]5=1 At the beginning, I said 1=5; therefore 5=1.[/spoiler]This seems pretty arbitrary to me.If you accept the idea that the solution is based on substitution, then you open up the possibility of a series of answers, each being equally valid. If 1=5 and 2=25, then 2=21. And 2=211. And 2=255 and 215 and 251. And if 4=4325, then 4=4325325255. All of these answers and an infinite number of other ones would be equally correct, it just depends on which substitutions you choose to make. ---
**Author:** ![Nancarrow](https://avatars.discourse-cdn.com/v4/letter/n/c37758/32.png) [@Nancarrow](https://boards.straightdope.com/u/Nancarrow)\ **Post date:** [September 19, 2015, 2:56pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/2 "2015-09-19T14:56:53Z")
Yeah, it sounds like a bloody stupid ‘gotcha’ to me. I’d have said your answer too. They want to be able to redefine the meaning of ‘=’ (essentially to mean “the number on the right is the pattern whose position in the sequence is the number on the left”) and then trick you at the end by saying “ha ha aren’t you thick for not knowing what ‘=’ means”? See also: “Do you know what the opposite of establishmentarianism is? Then spell it.” followed by chuckles all round as you fail to say “I-T”. ETA: to put it another way, the sort of person that would submit that as ‘an online math puzzle’ is the sort of person who could never, by any stretch of the imagination, be described as a ‘mathematician’. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 19, 2015, 5:40pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/3 "2015-09-19T17:40:52Z")
The very first line of the puzzle makes it clear that “=” does not have its usual meaning. It’s implied that it means “corresponds to”, or something like that, but we don’t know exactly what. And since we don’t know what it means, there’s no reason to assume that it’s commutative. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [September 19, 2015, 5:55pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/4 "2015-09-19T17:55:48Z")
> [@Chronos](#): > > The very first line of the puzzle makes it clear that “=” does not have its usual meaning. It’s implied that it means “corresponds to”, or something like that, but we don’t know exactly what. And since we don’t know what it means, there’s no reason to assume that it’s commutative. Agreed. If the “=” did have its usual meaning, “1=5” would be a false statement, and logically, _any_ conclusion could follow “If 1=5…” Now, if the “=” were understood to be an unspecified [equivalence relation](http://mathworld.wolfram.com/EquivalenceRelation.html), we could then assume symmetry, and “5=1” would be a correct answer, though not the only one possible. ---
**Author:** ![Ulf\_the\_Unwashed](https://avatars.discourse-cdn.com/v4/letter/u/b4bc9f/32.png) [@Ulf\_the\_Unwashed](https://boards.straightdope.com/u/Ulf_the_Unwashed)\ **Post date:** [September 19, 2015, 6:40pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/5 "2015-09-19T18:40:11Z")
> [@Chronos](#): > > The very first line of the puzzle makes it clear that “=” does not have its usual meaning. It’s implied that it means “corresponds to”, or something like that, but we don’t know exactly what. And since we don’t know what it means, there’s no reason to assume that it’s commutative. Or we are redefining 1 and/or 5, in which case there isn’t enough information to answer the question definitively either. It’s “puzzles” like these that give “math puzzles” a bad name. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [September 21, 2015, 4:32pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/6 "2015-09-21T16:32:41Z")
I agree it’s a poor puzzle. I would have phrased it: If first =5 second =25 third=325 fourth=4325 what does fifth=??? ---
**Author:** ![Your\_Great\_Darsh\_Face](https://avatars.discourse-cdn.com/v4/letter/y/ac8455/32.png) [@Your\_Great\_Darsh\_Face](https://boards.straightdope.com/u/Your_Great_Darsh_Face)\ **Post date:** [September 21, 2015, 5:30pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/7 "2015-09-21T17:30:06Z")
Yes, it’s a poor use of the equality sign, and an actual mathematician would write something like: f(1) = 5 f(2) = 25 f(3)= 325 f(4) = 4325 when it’s possible that f(5) = 1 all along but it certainly doesn’t follow from what’s shown. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [September 21, 2015, 5:37pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/8 "2015-09-21T17:37:27Z")
I’ve seen puzzles like this where the LHS and RHS are in different bases, but that doesn’t work in this situation. ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [September 21, 2015, 6:10pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/9 "2015-09-21T18:10:25Z")
And we have no evidence that ‘=’ represents an equivalence relation here. In particular, we don’t know it’s symmetric: we don’t know that a=b =\> b=a. And what **Nancarrow** said: > [@Nancarrow](#): > > Yeah, it sounds like a bloody stupid ‘gotcha’ to me. I’d have said your answer too. They want to be able to redefine the meaning of ‘=’ (essentially to mean “the number on the right is the pattern whose position in the sequence is the number on the left”) and then trick you at the end by saying “ha ha aren’t you thick for not knowing what ‘=’ means”? ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 21, 2015, 6:33pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/10 "2015-09-21T18:33:33Z")
My feeling is that once you’ve solved the logic of the puzzle, there should be a unique solution. If the system allows you to achieve multiple solutions which are all valid, then it’s worthless. I also agree that there’s no reason to assume reversability in this puzzle. Obviously 1 cannot equal 5 so we have to assume that the = means “results in”. But there’s no reason to assume the process of one resulting in five also means five results in one. Consider this sequence as an example: 1=1 3=9 5=25 7=49 9=? The system is obvious. It should be clear the correct answer is 81 not 3. ---
**Author:** ![Karen\_Lingel](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karen_lingel/32/18649_2.png) [@Karen\_Lingel](https://boards.straightdope.com/u/Karen_Lingel)\ **Post date:** [September 22, 2015, 1:17am UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/11 "2015-09-22T01:17:54Z")
For me, I read “if 1=5” as “false”, and ignore the whole “then” section. When asked 5=?, I say 5=5. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [September 23, 2015, 1:30am UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/12 "2015-09-23T01:30:30Z")
> [@Karen\_Lingel](#): > > For me, I read “if 1=5” as “false”, and ignore the whole “then” section. When asked 5=?, I say 5=5. Interesting take. Arguably, you could say that the system being used is all of the equalities are false. 1 doesn’t equal 5, 2 doesn’t equal 25, 3 doesn’t equal 325, and 4 doesn’t equal 4325. So by that logic, the answer to 5=? should be any number except 5. ---
**Author:** ![magnusblitz](https://avatars.discourse-cdn.com/v4/letter/m/b4bc9f/32.png) [@magnusblitz](https://boards.straightdope.com/u/magnusblitz)\ **Post date:** [September 24, 2015, 5:31am UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/13 "2015-09-24T05:31:43Z")
I agree, this seems pretty dumb. Especially because it later reuses other numbers (2=25, 3=325, 4=4325), etc. If we’re saying that 1=5 like they’re algebra variables, then it seems the same rule would apply to the other ones, which doesn’t make sense (4=4325 then means 4=4325325, but there’s still a 4, so it just replaces itself exponentially?). The fact that there is also an obvious “pattern” solution (54325) also makes it seem like they were trying for a bullshit “gotcha” question. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [September 24, 2015, 5:39am UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/14 "2015-09-24T05:39:34Z")
> [@Nancarrow](#): > > Yeah, it sounds like a bloody stupid ‘gotcha’ to me. I’d have said your answer too. They want to be able to redefine the meaning of ‘=’ (essentially to mean “the number on the right is the pattern whose position in the sequence is the number on the left”) and then trick you at the end by saying “ha ha aren’t you thick for not knowing what ‘=’ means”? > > See also: “Do you know what the opposite of establishmentarianism is? Then spell it.” followed by chuckles all round as you fail to say “I-T”. > > ETA: to put it another way, the sort of person that would submit that as ‘an online math puzzle’ is the sort of person who could never, by any stretch of the imagination, be described as a ‘mathematician’. Yes, it’s the math puzzle equivalent of that old “there are three words ending in gry…” ‘riddle’. Or those gotcha lateral thinking puzzles like “A man was in the hospital on the elevator going to visit his wife. How did he know she died?” Where there are a billion and one possible answers given only that information, but the asker acts all smug when you don’t get the specific one they settled on like “she was on life support and the elevator stopped because the power went out.” (Never mind that hospitals tend to have backup power for life support) As the quote goes, [“Communicating badly and then acting smug when you’re misunderstood is not cleverness.”](https://xkcd.com/169/) ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [September 27, 2015, 3:11am UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/15 "2015-09-27T03:11:23Z")
This reminds me of a very basic programming test used to weed out those who apparrently cannot learn to program. They don’t test for correctness, just that you are consistent. ```auto int a = 10; int b = 20; a = b; ``` One group argued the last line was invalid. I wonder if they wrote this puzzle… ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [September 30, 2015, 11:37pm UTC](https://boards.straightdope.com/t/is-the-answer-to-this-math-puzzle-legit/731768/16 "2015-09-30T23:37:55Z")
I agree completely with your answer (which is the one I would have given too) and your analysis.