My nephew brought home a menacing maths problem

I don't understand this. There is a solution, that the problem is unsolvable. It's as much a solution as finding a valid permutation would have been. It just sounds like his nephew hadn't yet learned that proving unsolvability means solving the problem.

In python: https://gist.github.com/ovolve/77e336ab05fda2aa25ebce8a33677...

Now the student knows that, really, all problems in math are of the form prove or disprove unless the statement is to prove in which case it is misleading to have the claim false. But, in texts, there can be errors, and a student needs to know that.

In college, I was reading a book on group theory and could not confirm a statement in the book. Some hours went by, and I couldn't get it. Eventually we found a counterexample and concluded that the book had an error. Actually, it was just an error in typography, a typo.

Later, on a Ph.D. qualifying exam, I struggled too long with a problem and got a failing grade. Yup, the problem asked for a proof, but the claim was false. There was a typo. I appealed, got an oral makeup exam in front of several profs, some angry, and ended with a "High Pass".

IIRC, Halmos, Finite Dimensional Vector Spaces just states that all the exercises are of the form prove or disprove. He goes on to say, "then discuss such changes in the hypotheses and/or conclusions that will make the true ones false and the false ones true".

At one point one course, for some early homework, my submission was that nearly all the exercises were false -- I'd found that the claims failed on the empty set! Given that the course started out with such sloppy work, I dropped it.

Net, really, in general in practice in math, all the statements, due to errors, typos, or whatever, have to be regarded as of the form prove or disprove.

i think it would have been kinder to to do 123 and 900 while also offering the possibility of choosing that it is impossible to achieve

i also disagree with the op's tactic of 'proving' this

this attempt to do less work to show the impossibility of the problem furthers the math education fallacy that numbers are material stead an abstraction

his method would falter in any other base

in research this reasoning is great at limiting a problem's scope but is useless as evidence in a proof, for instance: primes must end in 1,3,7, or 9, but to say any number ending in those digits is prime is clearly false..also 2,5 :p

i like the question the teacher offered but i think it is more appropriate in the math education i have been touting as the necessary future: teach the student to write a program that builds every possible iteration, adds them, then sorts the sums, then search for your desired value

learning math and programming together

it's long time to free our thoughts from rote arithmetic so we can think about larger implications and further abstractions more readily

i find it difficult to accept that the teacher truly just moved on without discussing this problem, that reads more as an excuse to write this post, but if it is true that is a ridiculous failure on the part of the teacher

also, offer kids real open questions stead some trick question, when i was in school i used to say to my math teachers 'why should i do these problems? you already know the answers' they treated me like a jerk, now that mindset is how i direct my research

From the problem statement, you know that 0 and 9 exist, so that eliminates binary through Base 9. But perhaps this hints at a more broad question: can 9000 be arrived at in any numeric base (> 10)?

3124

3124

1432

1324