I was taking an online math puzzle. One of the questions was this:
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.
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’.
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, we could then assume symmetry, and “5=1” would be a correct answer, though not the only one possible.
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.
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.
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.
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.
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)
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.
int a = 10;
int b = 20;
a = b;
One group argued the last line was invalid. I wonder if they wrote this puzzle…