
Ridiculous Math Problems - martinlaz
http://www.dam.brown.edu/people/mumford/blog/2020/Ridiculous.html
======
godelski
For more ridiculous math problems I want to submit: _The Jewish Problems_ [0].

These were used when Jewish people were trying to get into grad school in
Russia in the '70's. Basically designed so Jewish people wouldn't get in.

[0] [https://arxiv.org/abs/1110.1556](https://arxiv.org/abs/1110.1556)

~~~
agumonkey
Did this cause a toxin like stimulation making jewish students better because
they tried to reach impossible goals ?

It happened in music a few times.. people invented techniques and subgenres
because they tried impossible things or had below useful instruments.

~~~
hintymad
I doubt it. Those problems are close to impossible to solve for ordinary
students, therefore many talented but not necessarily genius students lost the
opportunity to get good education. I'm a firm believer that students need to
be pushed to stay in their discomfort zone, but Jewish Problems can easily
push most students into panic zone.

~~~
elbear
That's one of the principles of deliberate practice: go just beyond the
comfort zone, in the area where you feel a challenge, but an approachable one.

~~~
nordsieck
The point of the Jewish Problems is that:

1\. They're an entrance exam. They were explicitly designed to discriminiate
against otherwise worthy candidates.

2\. The key feature of the problems is that they are not difficult because
they are an average example of a difficult branch of math. Instead they are
easy problems, but they are only easy if you can figure out the correct
substitution. Otherwise, they are extremely difficult. In other words, getting
good at the problems won't make you a better mathematician, it'll just make
you better at passing that particular test.

~~~
elbear
I was only agreeing with the parent that students need to pushed out of their
comfort zone, but just a little. Not a lot like the Jewish Problems were
doing.

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mike00632
Reminds me of the cute banana, apple, pineapple math challenge that is
actually an elliptic curve.

[https://www.quora.com/How-do-you-find-the-positive-
integer-s...](https://www.quora.com/How-do-you-find-the-positive-integer-
solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4)

------
dan-robertson
A ridiculous problem I remember seeing was approximately this one:

    
    
      a/(b+c) + b/(a+c) + c/(a+b)=896.
      a,b,c positive integers
    

I think it probably used random symbols instead of letters and didn’t have the
integer requirement. Indeed if you allow real numbers or 0 then it is easy to
find a solution. I think it didn’t go particularly viral because it was too
hard. I think there’s a slightly easier version if you replace 896 by 16.

~~~
contravariant
The version I first saw used '4' instead of '896'. Which frankly made the
answer large enough that no reasonable amount of brute force could find it.

A good write up can be found here: [https://www.quora.com/How-do-you-find-the-
positive-integer-s...](https://www.quora.com/How-do-you-find-the-positive-
integer-solutions-to-frac-x-y%2Bz-%2B-frac-y-z%2Bx-%2B-frac-
z-x%2By-4/answer/Alon-Amit)

~~~
kens
That is an amazing, detailed explanation. (Don't be fooled by the quora
location.) Spoilers: the solution to the equation is 80-digit numbers, which
can be obtained by using elliptic curves, which the link explains in detail.

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murgindrag
There's a difference between a ridiculous math programs (which are often
amusing) and incorrect ones (for example, adding different units, or absolute
units rather than relative ones).

The article mixes the two.

One type is funny and clever.

The other type reinforces misconceptions and is damaging to students.

------
arkitaip
This reminds me of the riddle by the good soldier Svejk:

\-----

"Would you know how to calculate the diameter of the globe?"

"No, I'm afraid I wouldn't," answered Svejk, "but I'd like to ask you a riddle
myself, gentlemen. Take a three-storied house, with eight windows on each
floor. On the roof there are two dormer windows and two chimneys. On every
floor there are two tenants. And now, tell me, gentlemen, in which year the
house-porter's grandmother died?"

\-----

[https://english.radio.cz/good-soldier-svejk-a-literary-
chara...](https://english.radio.cz/good-soldier-svejk-a-literary-character-a-
legend-8072464)

~~~
pgtan
Which reminds me of the riddles in Yerofeyev's Moscow—Petushki (sorry, only in
russian, my russian and my english are too bad to translate)

«Знаменитый ударник Алексей Стаханов два раза в день ходил по малой нужде и
один раз в два дня – по большой. Когда же с ним случался запой, он четыре раза
в день ходил по малой нужде и ни разу – по большой. Подсчитай, сколько раз в
год ударник Алексей Стаханов сходил по малой нужде и сколько по большой нужде,
если учесть, что у него триста двенадцать дней в году был запой».

«Когда корабли Седьмого американского флота пришвартовались к станции Петушки,
партийных девиц там не было, но если комсомолок называть партийными, то каждая
третья из них была блондинкой. По отбытии кораблей Седьмого американского
флота обнаружилось следующее: каждая третья комсомолка была изнасилована;
каждая четвертая изнасилованная оказалась комсомолкой; каждая пятая
изнасилованная комсомолка оказалась блондинкой; каждая девятая изнасилованная
блондинка оказалась комсомолкой. Если всех девиц в Петушках 428 – определи,
сколько среди них осталось нетронутых беспартийных брюнеток?»

And my favorite:

«Как известно, в Петушках нет пунктов А. Пунктов Ц тем более нет. Есть одни
только пункты Б. Так вот: Папанин, желая спасти Водопьянова, вышел из пункта
Б1 в сторону пункта Б2. В то же мгновенье Водопьянов, желая спасти Папанина,
вышел из пункта Б2 в пункт Б1. Неизвестно почему оба они оказались в пункте
Б3, отстоящем от пункта Б1 на расстоянии 12-ти водопьяновских плевков, а от
пункта Б2 – на расстоянии 16-ти плевков Папанина. Если учесть, что Папанин
плевал на три метра семьдесят два сантиметра, а Водопьянов совсем не умел
плевать, выходил ли Папанин спасать Водопьянова?»

~~~
acqq
Using Google Translate doesn't produce anything understandable. But searching
for the text of the "favorite" part it can be seen that is is from this work:

[https://en.wikipedia.org/wiki/Moscow-
Petushki](https://en.wikipedia.org/wiki/Moscow-Petushki)

------
praptak
My math teacher used to give us silly problems like how long will it take the
raising water level to reach the top step of a ladder hanging down from a
ship. It trained us not to apply formulas blindly.

~~~
em-bee
it depends on the size of the hole at the bottom of the ship

------
kazinator
> _Well this is a bizarre 4th degree polynomial equation, \\(x^4-2x^2
> -400x=9999\\) and he applies one approach to solving it, then comes to a
> dead end and says "Hence ingenuity is called for" and finally finds that his
> unknown number is 11. I, personally, would not have had a clue how to solve
> it._

Here is what you can do. If there is an integer solution, we can keep the
constant term 9999 on the opposite side and factor the formula.

As in:

    
    
       x^4 - 2x^ - 400x = 9999
    
      x(x^3 - 2x - 400) = 9999
    
    

Ok, so no we have x f(x) = 9999. From this we know that if there is an integer
solution for x, x itself must be a factor of 9999: either a prime factor, or a
product of factors.

So we just factor 9999:

    
    
       3^2 11 101 = 9999
    

9999 has 3 as a degree 2 factor, and then also 11, and 101.

Looking at just the factorization breakdown alone, x could be the product of
these combinations of factors: { (3), (11), (101), (3, 3), (3, 11), (3, 101),
(11, 101), (3, 3, 11), (3, 3, 101), (3, 11, 101) }.

If we substitute these factors for x, in order from least to greatest, we will
soon hit upon the solution.

Intuitively we can guess that x is small, because the opposite factor is
cubing it. So for instance, it can't be the case that x is the product of 3,
11, and 101, such that x^3 - 2x - 400 then works out to the remaining factor
of 3.

It's obvious that x can't be too small, like 3, because x^3 is only 27; that's
not going to leave us a positive factor when we subtract 400 alone, let alone
-2x.

------
raister
"If a ship has 26 sheep and 10 goats on board, how old is the ship's captain?"

oh boy

~~~
cyptus
42

~~~
raister
Unfortunately, the actual answer is "there is not enough information on the
question to provide a response". It's an exercise as to the limits of problem
formulation, from what I understood.

~~~
cyptus
are you sure?

[https://www.google.com/search?q=answer+to+the+ultimate+quest...](https://www.google.com/search?q=answer+to+the+ultimate+question+of+life%2C+the+universe%2C+and+everything)

------
nephanth
Not about algebra, but one good example of ridiculous problems leading to
great discoveris in math is how, according to the legend, Cauchy invented
complex analysis (at least the theorems on holomorphic and meromorphic
functions) just to solve some random integral somebody had given him

------
Quekid5
My personal favorite along these lines are the Busy Beaver numbers. It's not
just huge... it's actually impossible to calculate (beyond very low inputs).

~~~
saagarjha
Impossible to _compute_ , only feasible to calculate for the first few.

~~~
Quekid5
Good correction, thanks! :)

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foolfoolz
the math equivalent of a dumb programming interview question

~~~
adrianmonk
The similarity extends to the part where the real motivation for asking is to
make the person asking look smart.

