15
$\begingroup$

It would be fun to have a puzzle "Find the only 10-digit number having each digit once AND property xyz", but offhand I don't know any "simple" xyz. "Is a square" gives far too many results, other powers don't work (up to 10). "Is prime" of course is an epic fail. Do you know any puzzle of this type? "Smallest/Largest such" is cheating :-)

$\endgroup$

1 Answer 1

22
$\begingroup$

Here is an example of what you are looking for

Find the only 10-digit number having each digit once such that the number formed by the first $n$ digits is divisible by $n$, for each $n$ from $1$ to $10$.

I'll leave it to the reader to find it for themselves.

$\endgroup$
6
  • 1
    $\begingroup$ That is a very nice property! 💖 $\endgroup$ Mar 23 at 21:12
  • $\begingroup$ This is the example I immediately thought of, too. $\endgroup$
    – Oliphaunt
    Mar 23 at 23:28
  • $\begingroup$ Now that you say, I immediately remember it :-) $\endgroup$ Mar 24 at 11:39
  • 1
    $\begingroup$ Meta-Problem: Does this only work in base 10? I hacked together a Python code, no or more than 1 solution in all bases<10 (except unary or binary) or 11. 12 is already too slow for me. $\endgroup$ Mar 24 at 19:59
  • 1
    $\begingroup$ @HaukeReddmann Some conditions on possible solutions in other bases b. b must be even for any solutions to exist. Odd digits must go in odd places and even digits in even places. The b/2th place is always b/2. $\endgroup$ Mar 25 at 0:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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