The Hardest Maths Questions You'll Ever Try

  • Thread starter Doomotron
  • 97 comments
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Danoff
That's what makes the question hard! The answer is yes. Follow me here. ;)



So we know that Z is 26, A is 1, and X is 24. We're asked to take the following as premises:

A=1
Z=26
X=24
Z-A=X

Our first step of logical evaluation is then to substitute the number for the letters

26-1=24

Consolidating, that's:

25=24

Here, we've shown a contradiction. That A equals not A. According to the principle of explosion, anything follows a contradiction. So we can conclude A+Z=X, or anything we'd like from these contradictory premises. That's not as hard as the navier stokes equations though.
Click to expand...


I'm not answering a question in this post, it's too early in the morning and I haven't had some coffee yet, but @Danoff , you still haven't read my original post properly. I am literally re-skinning numbers as letters, so if you go past 9 (Or more like 26), you get double numbers (10), or in this case AA as there is no 0.
 
Doomotron
I'm not answering a question in this post, it's too early in the morning and I haven't had some coffee yet, but @Danoff , you still haven't read my original post properly. I am literally re-skinning numbers as letters, so if you go past 9 (Or more like 26), you get double numbers (10), or in this case AA as there is no 0.
Click to expand...
You haven't read your own question. @Danoff & @SlipZtrEm explained this to you.
A is a letter, to which you have given the value of "1".
Z is a letter, to which you have given the value of "26".
You told us that Z-A=X, or 26-1=X, so X=25.
Unfortunately X is a letter, to which you have given the value of "24".
So the initial part of your question tells us that 25=24.
Once you're redefining numbers to other numbers, anything could be true. So yes, A+Z could equal X. Or Q. Or A. Or WOMBAT.

Of course since then you've edited your post so that Z-A=X is now Z-B=X, so you're fully aware that there was a problem with your 'hard' math question - in that it was nonsense. Not sure why you're pretending otherwise.
 
Famine
You haven't read your own question. @Danoff & @SlipZtrEm explained this to you.
A is a letter, to which you have given the value of "1".
Z is a letter, to which you have given the value of "26".
You told us that Z-A=X, or 26-1=X, so X=25.
Unfortunately X is a letter, to which you have given the value of "24".
So the initial part of your question tells us that 25=24.
Once you're redefining numbers to other numbers, anything could be true. So yes, A+Z could equal X. Or Q. Or A. Or WOMBAT.

Of course since then you've edited your post so that Z-A=X is now Z-B=X, so you're fully aware that there was a problem with your 'hard' math question - in that it was nonsense. Not sure why you're pretending otherwise.
Click to expand...
So, in short: Syntax error. Does not compute! Does not compute! *head explodes*
 
Vegard
So, in short: Syntax error. Does not compute! Does not compute! *head explodes*
Click to expand...

It does compute, it's just that the initial 'if' statement is false, so we never move on to evaluate if Z+A=X. After all, the question asks us to evaluate the second statement only if the first statement is true.

So the correct answer is that there is no question to answer.

Code: 
>>> A = 1
>>> X = 24
>>> Z = 26
>>> if Z-A==X: Z+A==X

 
>>>
 
Last edited:
Famine
You haven't read your own question. @Danoff & @SlipZtrEm explained this to you.
A is a letter, to which you have given the value of "1".
Z is a letter, to which you have given the value of "26".
You told us that Z-A=X, or 26-1=X, so X=25.
Unfortunately X is a letter, to which you have given the value of "24".
So the initial part of your question tells us that 25=24.
Once you're redefining numbers to other numbers, anything could be true. So yes, A+Z could equal X. Or Q. Or A. Or WOMBAT.

Of course since then you've edited your post so that Z-A=X is now Z-B=X, so you're fully aware that there was a problem with your 'hard' math question - in that it was nonsense. Not sure why you're pretending otherwise.
Click to expand...

Vegard
So, in short: Syntax error. Does not compute! Does not compute! *head explodes*
Click to expand...
More like:
++?????++ Out of Cheese Error. Redo From Start.
 
AspecBob
Using only the four basic operations (+, -, *, /), the numbers 1, 5, 6 and 7, and as many parentheses as you want, make 21. (Each of the four numbers must be used once.)
Click to expand...
6/(1-5/7)
I solved it with brute computer force and a little python script that checks all possible combinations:
Code: 
import itertools as it
import operator as op
ops=[op.add, op.sub, op.mul, op.truediv]
nums=[1,5,6,7]
for o in it.product(ops,repeat=3):
    for c in it.permutations(nums,4):
        try:
            o0=o[0](c[0],c[1])
            o1=o[1](c[2],c[3])
            o2=o[2](o0  ,o1)
            x = abs(o2)
            if x < 21.1 and x > 20.9:
                print('found 1',x,o,c)
            o1=o[1](o0,  c[2])
            o2=o[2](o1,  c[3])
            x = abs(o2)
            if x < 21.1 and x > 20.9:
                print('found 2',x,o,c)
            o1=o[1](o0,  c[2])
            o2=o[2](c[3],  o1)
            x = abs(o2)
            if x < 21.1 and x > 20.9:
                print('found 3',x,o,c)
            o1=o[1](c[2], o0)
            o2=o[2](o1, c[3])
            x = abs(o2)
            if x < 21.1 and x > 20.9:
                print('found 4',x,o,c)
        except:
            pass

Love these brain teasers, here is one involving the @Doomotron numerals (A stands for 1, B stands for 2, ..., 26 stands for Z): NERD is a Doomotron numeral for the number 5040=14*5*18*4=N*E*R*D. Can you find another valuable 4 letter numeral for the same number? Only multiplication allowed: No A+B+C+D please! :D
 
Last edited:
Vegard
So, in short: Syntax error. Does not compute! Does not compute! *head explodes*
Click to expand...
chef_bot___does_not_compute__by_giframa-d555wi8.gif
 
So it's wrong and it's in Base 9?

Doomotron
I'm not answering a question in this post, it's too early in the morning and I haven't had some coffee yet, but @Danoff , you still haven't read my original post properly. I am literally re-skinning numbers as letters, so if you go past 9 (Or more like 26), you get double numbers (10), or in this case AA as there is no 0.
Click to expand...

AA would be 11, not 10. There is no zero? You're just making things up now. You can't do that!

 
Omnis
AA would be 11, not 10. There is no zero? You're just making things up now. You can't do that!
Click to expand...

AA would be 27 with positional interpretation, AA=1*26+1=27. But without a zero you have problems with a number like 677 = 1*26*26+0*26+1, you need a placeholder like _ to show the first A in A_A means 1*26*26. The Babylonians had no zero, but a placeholder in their numeral system. But why bother with that, just multiply and add your one letter numbers to form new ones, ignore uniqueness of your numerals and have fun with numbers. :sly:

Here is another brain teaser for you math geeks, got that from an old journal:

A colony of chameleons contains 20 red, 18 green and 16 blue individuals. Every time two chameleons of different colors meet, they both switch colors to the third color none of them has at the moment. Some time passes, during which no chameleon dies, is born, enters or leaves the colony. Is it possible that at the end of this period all 54 chameleons have the same color?
 
tarnheld
A colony of chameleons contains 20 red, 18 green and 16 blue individuals. Every time two chameleons of different colors meet, they both switch colors to the third color none of them has at the moment. Some time passes, during which no chameleon dies, is born, enters or leaves the colony. Is it possible that at the end of this period all 54 chameleons have the same color?
Click to expand...

No. After figuring it out on my own through trial and error, I googled the way to actually describe how that is, mathematically. It's not a method I'm familiar with, but my own reasoning was that I'd always be stuck with differences that weren't divisible by 3. There needs to be a difference of 3 between any two colours to allow for the necessary balancing to lead to a single-colour outcome.
 
tarnheld
AA would be 27 with positional interpretation, AA=1*26+1=27. But without a zero you have problems with a number like 677 = 1*26*26+0*26+1, you need a placeholder like _ to show the first A in A_A means 1*26*26. The Babylonians had no zero, but a placeholder in their numeral system. But why bother with that, just multiply and add your one letter numbers to form new ones, ignore uniqueness of your numerals and have fun with numbers. :sly:

Here is another brain teaser for you math geeks, got that from an old journal:

A colony of chameleons contains 20 red, 18 green and 16 blue individuals. Every time two chameleons of different colors meet, they both switch colors to the third color none of them has at the moment. Some time passes, during which no chameleon dies, is born, enters or leaves the colony. Is it possible that at the end of this period all 54 chameleons have the same color?
Click to expand...


Those aren't numbers because numbers make sense. BTW, base 12... Is 10 ten or twelve?
 
Aren't the hardest math problems ones like these? Like... ones that even mathematicians haven't been able to figure out?
 
Yes, and for some of them it's not even known yet whether they are solvable!

I suppose the focus here, in this thread, should be on medium to hard problems that are still doable with pen and paper...
 
Crash
Aren't the hardest math problems ones like these?
Click to expand...

The hardest math problem is the one you want to solve right now but can't. ;) To tackle the millenium problems you'd need a year or two just to understand the problem and the failed attempts to solve it. :eek: And the solution wouldn't be that exciting at all, the way of solving and the tools developed for that would be way more exciting -- just like the problems presented here. The solution can be easily checked once you found it (hopefully not with googling), but the excitement while working up your way to a solution is the real kick. :D

Here is another one:

A fox travels one mile south. Then he turns east and travels again one mile. Here he turns left, walks one mile due north and arrives at the same point he left in the beginning. What color has the fox?

The original linear system has a solution too, they are just not integers:
Code: 
linsolve([5*x +3*y +2*z =11, -3*x +2*x -7*z =-26, 8*x -y +z =3], [x,y,z]);
[x=5/99,y=10/9,z=367/99]
But hey, they are still rational! :) I hated these assignments in school, so many ways to make errors in the calculation steps, and if the answers were not integers you knew you made a mistake in your calculation. :ouch: Hooray for computer algebra systems, computers are made for that kind of questions! 👍
 
tarnheld
The hardest math problem is the one you want to solve right now but can't. ;) To tackle the millenium problems you'd need a year or two just to understand the problem and the failed attempts to solve it. :eek: And the solution wouldn't be that exciting at all, the way of solving and the tools developed for that would be way more exciting -- just like the problems presented here. The solution can be easily checked once you found it (hopefully not with googling), but the excitement while working up your way to a solution is the real kick. :D

Here is another one:

A fox travels one mile south. Then he turns east and travels again one mile. Here he turns left, walks one mile due north and arrives at the same point he left in the beginning. What color has the fox?
Click to expand...







Green. The shape he makes from his travels is a triangle, then you get the Illuminati symbol, which is green. I easily solved that since I know ten-year-olds who are always drawing those symbols on their tests. I wonder what grade they got for that test...
 
eran0004
It does compute, it's just that the initial 'if' statement is false, so we never move on to evaluate if Z+A=X. After all, the question asks us to evaluate the second statement only if the first statement is true.

So the correct answer is that there is no question to answer.

Code: 
>>> A = 1
>>> X = 24
>>> Z = 26
>>> if Z-A==X: Z+A==X


>>>
Click to expand...

Get that sorcery out of here, I've done enough coding for a day.
 
tarnheld
A fox travels one mile south. Then he turns east and travels again one mile. Here he turns left, walks one mile due north and arrives at the same point he left in the beginning. What color has the fox?
Click to expand...
Probably white.
 
I think the real question isn't what color it was, but what does the fox say?
 
tarnheld
A fox travels one mile south. Then he turns east and travels again one mile. Here he turns left, walks one mile due north and arrives at the same point he left in the beginning. What color has the fox?
Click to expand...

Brown or white.

Minty
I think the real question isn't what color it was, but what does the fox say?
Click to expand...

Not this crap again.

I would provide the translation to geekering but it is against the AUP.
 
mcsqueegy
You made a typo in the question. Assuming you meant:



Then the answer is

x=0, y=1, z=4
Click to expand...

tarnheld
The hardest math problem is the one you want to solve right now but can't. ;) To tackle the millenium problems you'd need a year or two just to understand the problem and the failed attempts to solve it. :eek: And the solution wouldn't be that exciting at all, the way of solving and the tools developed for that would be way more exciting -- just like the problems presented here. The solution can be easily checked once you found it (hopefully not with googling), but the excitement while working up your way to a solution is the real kick. :D

Here is another one:

A fox travels one mile south. Then he turns east and travels again one mile. Here he turns left, walks one mile due north and arrives at the same point he left in the beginning. What color has the fox?

The original linear system has a solution too, they are just not integers:
Code: 
linsolve([5*x +3*y +2*z =11, -3*x +2*x -7*z =-26, 8*x -y +z =3], [x,y,z]);
[x=5/99,y=10/9,z=367/99]
But hey, they are still rational! :) I hated these assignments in school, so many ways to make errors in the calculation steps, and if the answers were not integers you knew you made a mistake in your calculation. :ouch: Hooray for computer algebra systems, computers are made for that kind of questions! 👍
Click to expand...

@mcsqueegy is correct, and yeah, that was a typo.
 
Grayfox
Brown or white.
Click to expand...
It would be brown or white only if it's (more or less) native to one of the two regions where this can occur. Somebody could have dropped off a red fox in the area, for instance. That's why I qualified my answer with "probably". Of course there are no foxes native to the other region where this can occur.
 

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