# Maths dopers- a puzzle from childhood **URL:** \ **Category:** Factual Questions\ **Created:** [May 14, 2003, 9:59am UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167 "2003-05-14T09:59:32Z")\ **Posts on this page:** 13\ **Page:** 3
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 14, 2003, 9:18pm UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/41 "2003-05-14T21:18:32Z")
What happened to (0, Y, 1, X)? ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [May 14, 2003, 9:48pm UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/42 "2003-05-14T21:48:03Z")
> [@](#): > > What happened to (0, Y, 1, X)? It’s just a reflection of (0, X, 1, Y). ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 14, 2003, 9:49pm UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/43 "2003-05-14T21:49:26Z")
OK. ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [May 15, 2003, 3:18am UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/44 "2003-05-15T03:18:05Z")
> [@](#): > > \*Originally posted by ZenBeam \* > \*\*Actually, there are several such “extra large” jumps, the first between 23 and 24. Are these lists minimal solutions? > \*\* The “extra large” jumps occur earlier in the list as well. And, having allowed the program to run a bit longer, I can tell you that the solutions given up to 32 (1, 10610, 30123, 66013) are minimal solutions. There’s nothing like a bit of brute force. ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [May 15, 2003, 10:29am UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/45 "2003-05-15T10:29:50Z")
I’ve verified that **zut** ’s solutions up to 38 (1, 121416, 344733, 755477) are minimal. I don’t think I’ll do any more, it takes rather a lot of processor time. ---
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [May 15, 2003, 10:51am UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/46 "2003-05-15T10:51:57Z")
Looks like **zut** nailed it. Kudos to him _et al_. ---
**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\ **Post date:** [May 15, 2003, 11:39am UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/47 "2003-05-15T11:39:46Z")
One other thing of interest: this same problem is being discussed [here](http://www.greylabyrinth.com/Forums/Forum5/HTML/004839.html?15), and someone else pointed out that these sets of “squares” have a name: they’re called Ducci sequences. I gather a more general Ducci sequence has n numbers on each level (the one on this thread having n=4). There are [one](http://www.math.jussieu.fr/~flo/research.html) or [two](http://www.csam.montclair.edu/~thomasd/) or [three](http://www.loyola.edu/academics/academicaffairs/ayoung/papers.html) people that study these professionally. ---
**Author:** ![aahala](https://avatars.discourse-cdn.com/v4/letter/a/a88e4f/32.png) [@aahala](https://boards.straightdope.com/u/aahala)\ **Post date:** [May 15, 2003, 12:00pm UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/48 "2003-05-15T12:00:22Z")
Let’s do triangles.😃 I don’t understand half of it, but excellent links \zut.\ ---
**Author:** ![Shalmanese](https://avatars.discourse-cdn.com/v4/letter/s/45deac/32.png) [@Shalmanese](https://boards.straightdope.com/u/Shalmanese)\ **Post date:** [May 15, 2003, 12:03pm UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/49 "2003-05-15T12:03:36Z")
I can confirm those numbers up to n = 50. It looks to be correct. ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [May 15, 2003, 12:16pm UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/50 "2003-05-15T12:16:33Z")
What do you mean by “confirm those numbers”? That they are solutions, or that they are the smallest solutions? ---
**Author:** ![hammos1](https://avatars.discourse-cdn.com/v4/letter/h/ba8739/32.png) [@hammos1](https://boards.straightdope.com/u/hammos1)\ **Post date:** [May 15, 2003, 4:07pm UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/51 "2003-05-15T16:07:28Z")
Thanks to zut, and a big tip of the hat to Zenbeam for providing the analysis of the general case- great idea to reduce it to permutations of (0, X, Y, 1). I was about to suggest extension to shapes with n sides- but I see I’ve been pre-empted! ---
**Author:** ![Shalmanese](https://avatars.discourse-cdn.com/v4/letter/s/45deac/32.png) [@Shalmanese](https://boards.straightdope.com/u/Shalmanese)\ **Post date:** [May 18, 2003, 2:58am UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/52 "2003-05-18T02:58:50Z")
They are the smallest. ---
**Author:** ![emolson](https://avatars.discourse-cdn.com/v4/letter/e/5fc32e/32.png) [@emolson](https://boards.straightdope.com/u/emolson)\ **Post date:** [May 18, 2003, 4:50am UTC](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167/53 "2003-05-18T04:50:58Z")
A fairly simple problem, which turns out to be somewhat complex, which gets exhaustively examined unto death, … errr, I’ve gotten somewhat off the track. 😃 Thanks to all who participated in a fascinating diversion. [Previous page](https://boards.straightdope.com/t/maths-dopers-a-puzzle-from-childhood/175167.md?page=2)