1
$\begingroup$

We can cut any square on $n$ squares if $n>5$ and $n=4$.

The proof is easy by induction. Base cases $n=6,7,8$ are easy to find and then since we can cut a square on $4$ squares we get $3$ new squares, so we go from $n\to n+3$ and we are done.

But I can not find a proof that we can't cut it on $5$ squares. I suppose we should search for some contradiction, but...?

$\endgroup$
  • 3
    $\begingroup$ Here is the link for $n>5$. For $n=5$ see here. $\endgroup$ – Dietrich Burde Sep 22 '18 at 9:01
  • 3
    $\begingroup$ @DietrichBurde: The given link for $n=5$ is about decomposing and reassembling. I think that the latter is forbidden here. $\endgroup$ – Christian Blatter Sep 22 '18 at 9:31
2
$\begingroup$

The book Mathematical Olympiad Challenges by Titu Andreescu and Razvan Gelca (Birkhäuser 1967) contains a proof for the case $n=5$. Here is a screenshot from page 128:

enter image description here

$\endgroup$
2
$\begingroup$

If you had glue, @greedoid, it would be too easy: 5 squares from one

$\endgroup$
  • 2
    $\begingroup$ Thanks...........! +1 $\endgroup$ – Aqua Sep 22 '18 at 11:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.