uncrossed knight's tours in 3D uncrossed knight's tours [1,2] uncrossed camel's tours [1,3] uncrossed giraffe's tours [1,4] uncrossed zebra's tours [2,3] uncrossed antelope's tours [3,4]

open knight's tour of length 37 on chessboard 14x5
Author: unknown
Date (d/m/y): 01/08/2011
Path: 5858585858 5714141414 1414175858 5858585
M=(n-2)(m-2)-C = -1
k=C/nm = 0.529
Q=C-[(n-3)(m-3)+10] = 5
n=5; m=

2 paths for chessboard 14x5
37unknown01/08/20115858585858 5714141414 1414175858 5858585
36Makarova05/10/20113833833816 4774774747 6838253838 338338

Uncrossed closed knight's tours

Uncrossed open knight's tours

Last changes
Derek Kisman25/10/201831x20 (478) closed1161161161 1611618352 5525525525 5255225225 2252252252 2522522523 8616616616 6166166166 1661661161 1611611611 6134752552 5525525522 5225225225 2252252252 2528746166 1661661661 6616616611 6116116121 6832555525 5255225225 2252252252 2521253816 6661661661 6616616611 6116111383 5552552252 2522522522 3661661661 6616616611 6118552552 5522522522 5225225222 1616661661 6616616611 6111413655 2252252252 2522766166 1661661213 2324616767 5252252252 2835366616 6166166166 1185525522 5225225225 2225254545 4676166166 1661661661 66166166
Derek Kisman25/10/201831x21 (510) closed7182525252 5225225225 2252252252 2523861661 6616616616 6166166161 6161616116 1161161835 2552552552 5252525252 2522522522 5225225225 2874616616 6166166166 1661616161 6161161161 1613475255 2552525252 5252252252 2522522521 2538166661 6616616616 6161616161 6116121683 2555525252 5252522522 5225225222 1616661661 6616616161 6161855252 5252525225 2252252236 6166166166 1661616161 6161112352 5252525225 2252252276 6166166161 6161613247 5252522522 5287461661 8352134316 1683252546 6616616616 6161616161 7452525252 5225225225 2225254545 4676166166 1661661661 6616616164
Derek Kisman26/10/201831x22 (532) closed1161161161 1618352552 5525525522 5225225225 2252252252 2523861661 6616616616 6166166166 1161161161 1161647825 2252555255 2552552252 2522522522 5225225225 2874616616 6166166166 1661661161 1611611161 6616832522 5255525525 5255225225 2252252252 2521253816 6661661661 6616616611 6116116111 4652552552 5522522522 5225225222 1616661661 6616616611 6118552552 5522522522 5225223661 6616616616 6166116116 1112355255 2252252252 2522766166 1661661161 1324132575 2521383574 6166166166 1238675255 2252252252 2146366616 6166166166 1161174552 5522522522 5225222525 4545467616 6166166166 1661661661 66
Derek Kisman26/10/201831x23 (562) closed1161161161 1611611618 3525525525 5255255255 2252252252 2522522522 5225238616 6166166166 1661661661 6611611611 6116116116 1347525525 5255255255 2252252252 2522522522 5225287461 6616616616 6166166166 1161161161 1612168325 5552552552 5522522522 5225225225 2125381666 6166166166 1661661161 1611611123 5525525522 5225225225 2247661661 6616616611 6116117455 2552552252 2522522522 3661661661 6616616611 6116118552 5525525522 5225225225 2252221866 1661661661 6611611611 3425652252 2522522528 7461661661 6116832552 5225287461 6123257421 3585346616 6166166166 1161387525 5255225225 2252252245 4545467616 6166166166 1661661661 66
Derek Kisman30/10/201831x24 (586) closed1611611611 6116116116 1835255255 2552552552 5525225225 2252252252 2522522386 6166166166 1661661661 6616116116 1161161161 1613475255 2552552552 5525225225 2252252252 2522522766 1661661661 6616616616 1161161161 1612168325 5552552552 5525225225 2252252252 2522766166 1661661661 6616116116 1161112355 2552552522 5225225225 2252874616 6166166166 1611611611 3383255522 5225221747 4616616611 4252861338 3356661661 6611746525 2252252222 5471666616 6166161161 3875255255 2522522522 5212534661 6616616616 6166161161 1611745525 5255252252 2522522522 5224766166 1661661661 6616116116 1185525525 5255252252 2522522522 5223535474 7616616616 6166166166 166166
Derek Kisman30/10/201831x25 (608) closed1161161161 1611618352 5525525525 5255225225 2252252252 2522522523 8616616616 6166166166 1661661161 1611611611 1616478252 2525552552 5525525522 5225225225 2252252252 2528746166 1661661661 6616616611 6116116116 1116166168 3252252555 2552552552 5522522522 5225225225 2125381666 6166166166 1661661161 1611611611 4552552552 5522522522 5225225222 7561661661 6616616611 6116116111 6832555255 2552552252 2522522522 2272753666 1661661661 6611611611 6114552552 5522522522 5225227661 6616616611 6116118355 2552552252 2522522138 6561661661 6611611611 3425652252 2522766161 1683255252 2275616131 3366366616 6166116138 7525525522 5225222272 4546354545 4676166166 1661661661 66166166
Derek Kisman30/10/201831x26 (642) closed1161161161 1611611611 6183525525 5255255255 2552552252 2522522522 5225225225 2386166166 1661661661 6616616611 6116116116 1161161161 3475255255 2552552552 5522522522 5225225225 2252252874 6166166166 1661661661 6611611611 6116116121 6832555525 5255255255 2252252252 2522522521 2538166661 6616616616 6166116116 1161161112 3552552552 5522522522 5225224766 1661661661 6611611611 6117455255 2552552252 2522522522 3661661661 6616616611 6116116118 5525525525 5255225225 2252252252 2218661661 6616616611 6116116113 4256525522 5225225225 2874616616 6166111168 3255552252 2528746166 1112538383 2574747755 2133838314 5471747434 6616616616 6166116116 1387525525 5255225225 2252252245 4545467616 6166166166 1661661661 66
Derek Kisman01/11/201831x27 (668) closed1611611611 6116116116 1161835255 2552552552 5525525525 2252252252 2522522522 5223866166 1661661661 6616616616 1161161161 1611611611 6134752552 5525525525 5255252252 2522522522 5225225227 6616616616 6166166166 1611611611 6116116121 6832555525 5255255255 2522522522 5225225225 2276616616 6166166166 1611611611 6116111235 5255255255 2522522522 5225225287 4616616616 6166161161 1611611338 3255552522 5225221747 4616616616 1112355616 1317475525 2252811438 2547753833 5666166166 1611174652 5525225225 2222547166 6616616616 1161161387 5255255255 2522522522 5212534661 6616616616 6166161161 1611611745 5255255255 2522522522 5225225224 7661661661 6616616616 1161161161 1855255255 2552552522 5225225225 2252235354 7476166166 1661661661 66166166
Derek Kisman01/11/201827x24 (498) closed1161161161 8182525525 5255255255 2252252252 2522522522 3866166166 1661661661 6611611611 6116116161 6183525252 5525525525 5255225225 2252252252 2522766166 1661661661 6611611611 6116116161 6132475255 2552552552 5522522522 5225225227 6616616616 6166116116 1161161283 5552552552 5522522522 5225223866 1661661661 6611611611 6111413655 2552552252 2522522528 7461661661 6611611612 1325255252 2174746161 1335666161 1616655255 2252252138 6661661161 3825256522 5222254744 6616616616 6166116116 1185525525 5255225225 2252252245 4547476166 1661661661 66166166
Derek Kisman05/11/201831x28 (694) closed1161161161 1611611618 3525525525 5255255255 2252252252 2522522522 5225238616 6166166166 1661661661 6611611611 6116116111 6164782522 5255525525 5255255255 2252252252 2522522522 5225287461 6616616616 6166166166 1161161161 1611611161 6616832522 5255525525 5255255255 2252252252 2522522521 2538166661 6616616616 6166116116 1161161161 1141365525 5255255255 2252252252 2522366166 1661661661 6611611611 6116118552 5525525525 5255225225 2252252252 2216166616 6166166166 1161161161 1612141325 2255552252 2528746166 1112474755 2138383834 5465616616 6166116127 2255552252 2522281747 4466166166 1111666525 5255225225 2252214636 6616616616 6166116116 1161145525 5255225225 2252252276 6166166166 1161161127 5855525525 5255225225 2252252225 2545454676 1661661661 6616616616 6166
Derek Kisman05/11/201831x29 (724) closed1161161161 1611611611 6116183525 5255255255 2552552552 5522522522 5225225225 2252252386 1661661661 6616616616 6166116116 1161161161 1611611613 4752552552 5525525525 5255225225 2252252252 2522522528 7461661661 6616616616 6166116116 1161161161 1612168325 5552552552 5525525522 5225225225 2252252125 3816666166 1661661661 6611611611 6116116111 2355255255 2552552252 2522522522 4766166166 1661661161 1611611611 7455255255 2552552252 2522522522 3661661661 6616616611 6116116116 1185525525 5255255255 2252252252 2522522218 6616616616 6166116116 1161161134 2565255255 2252252252 2528746166 1661661161 1116832555 5255225225 2138666166 1161112413 2475585855 2252216135 6661661161 2414175865 5255225222 2547446616 6166166166 1161161161 3875255255 2552552252 2522522522 4545454676 1661661661 6616616616 6166
Derek Kisman05/11/201831x30 (738) closed1611611611 6116116116 1161835255 2552552552 5525525525 2252252252 2522522522 5223866166 1661661661 6616616616 1161161161 1611611611 1616478252 2525552552 5525525525 5255252252 2522522522 5225225227 6616616616 6166166166 1611611611 6116116116 1114136552 5525525525 5255252252 2522522522 5222728566 1661661661 6616116116 1161161145 5255255255 2522522522 5225212727 5366616616 6166161161 1611611275 8555255255 2552552522 5225225225 2236616616 6166166166 1611611611 6116116121 4132475652 5525525525 2252252252 2766166166 1611611611 1428235555 2522522272 7277446616 1145288555 2522366166 1611113383 4636366661 6616116121 7465525525 2252222476 5616616616 1161185525 5255252252 2522134546 3656166166 1661661661 6616116116 1161161161 1855255255 2552552552 5525225225 2252252252 2522146354 7476166166 1661661661 66166166

new knight's tour


to 10 comma-separated paths:

You can specify up to 10 paths, separated by commas

Each character in path is the direction from the last waypoint:

Sample path: 7531:

In parentheses are given by recurrence. The number after the closing parenthesis indicates the number of repetitions. For example 75 (85)9 3 (14)9 1 is translated into 75 858585858585858585 3 141414141414141414 1.

For symmetric open tours:

a) If the last character of the path is an asterisk, the path is repeated again in reverse order. For example 74774761383* is translated into 74774761383 38316747747.

b) If the last character of the path it is '>', the path is repeated again in reverse order without the last character. For example 1661661835225> is translated into 166166183522 5 225381661661.

p:19032 05/04/2015 Off-line version of this base (Windows only) (knighttoursbase.zip) (712.8 Кб, loaded: 18276 )
12.09.2011 09:53 Наталия
К симметричным маршрутам на полях 9х9 и 13х13 нужно приписать: ext. from R. Merson 15x15.
Маршрут на поле 12х16 введён как ext. from svb 20x24, нет автора (не умещается всё в поле для ввода). То же самое в маршруте на поле 19х27, введён как ext. from A. Chernov 11x19.

12.09.2011 10:21 alexBlack
Исправил ...

13.09.2011 09:49 Наталия
Я не попыталась всё ввести в поле для автора...
К несимметричным маршрутам 15х15, 23х23 и 31х31 надо добавить: ext. from Eric Bainville 7x7.
Может быть, вы расширите поле для ввода автора?.. Если это возможно.

13.09.2011 07:39 svb
Мне кажется, что до тех пор, пока нет программной реализации получения нового полученного кем-то маршрута, лучше ставить имя последнего \"реализатора\". В противном случае мы рискуем окончательно запутаться.

13.09.2011 08:04 alexBlack
Для 15х15, 23х23 и 31х31 информацию в скобках добавил.

Давайте придерживаться формата для имени, который уже есть в базе: указываем свое имя и, если нужно, в скобках описание маршрута, от которого получен результат. Например, Makarova (ext.from R.Merson 15x15).
Поле для ввода я увеличил, 40 символов должно хватить.

Выложил новую версию off-лайн базы. В этой версии в таблицах заголовки (где указаны m и n) являются переключателями. Щелчок мышки переключает отображение в таблицах количества/коэффициентов k и M.

13.09.2011 09:54 svb
Спасибо за новую версию off-лайн базы! Стало очень наглядно.

13.09.2011 11:39 Наталия
Алексей, вы видели все маршруты, которые я вводила сегодня как ext.from svb ...? Их было несколько, два или три, не помню точно.
По поводу \"реализотора\". У меня нет никакой путаницы. Если я делаю простой перенос маршрута с шагом 8 и ничего при этом не дорабатываю, то пишу, что маршрут получен от такого-то маршрута. Если же далаю доработки угловых фрагментов, то пишу своё имя. Всё очень просто.

14.09.2011 12:52 Наталия
Базу скачала. Спасибо. Все коэффициенты теперь видно.
Вот нашла один маршрут: поле 24х31, введён как ext.from svb 16x23, без имени автора. Ещё вроде один был. Если вы не увидите его, я позже найду.

14.09.2011 07:59 alexBlack
Исправил 24x31, 20x25, 12x17

15.09.2011 03:07 Наталия
Алексей, никак не могу ввести маршрут с таким авторством:
Makarova (ext.from svb 15x22)
Выходит ошибка:
Error: Invalid characters in name. Allowed only \"0-9 a-z . _ \"
Пробовала скопировать имя автора в вашем примере и ввести, ничего не дало, та же ошибка.

15.09.2011 03:15 Наталия
Ввела этот маршрут (поле 23х30) со своим авторством, без добавки на маршрут svb. Так сразу ввелось. Что я пишу в добавке не так?
Добавьте, пожалуйста, ссылку на маршрут svb (15х22).

15.09.2011 07:15 alexBlack
Забыл добавить скобочки в список допустимых символов. 23x30 исправил.

17.09.2011 09:05 Наталия
Алексей, я задала на форуме вопрос о тривиальных маршрутах. Сложно работать, когда на вопросы не отвечают. Вводить или нет тривиальные несимметричные маршруты?

17.09.2011 02:59 alexBlack
Наталия, если я не отвечаю, значит не знаю ответа. И потом, Вы сами ответили на этот вопрос. Я, как и Вы, думаю, что убрать один ход и получить новый маршрут - это слишком просто и вводить такие маршруты нет смысла. С другой стороны запрета на ввод таких маршрутов нет, нужно будет подумать как делать такую проверку при вводе данных.

17.09.2011 05:02 Наталия
Но откуда же мне знать, почему вы не отвечаете? Вы вчера вечером были на форуме. Нельзя было высказать своё мнение (вот это, которое вы высказали здесь) в теме? Или это тоже рабочий момент, который не следует обсуждать на форуме? Тогда, может быть, следует закрыть на форуме тему?

17.09.2011 05:07 Наталия
А по поводу тех маршрутов, в которых немного изменён один угловой фрагмент? Такие маршруты можно вводить? Я думаю, что этот вопрос вполне по теме и его можно было обсудить на форуме. Но ни вы, ни Сергей в тему больше не хотите писать. Ну, в таком случае я закрываю тему.

17.09.2011 06:10 alexBlack
Я не вижу, что здесь обсуждать (но это мое мнение и возможно кто-то из форумчан еще отпишется). Давайте вспомним изначальную постановку задачи - поиск максимального непересекающегося маршрута. Представляют ли интерес немаксимальные маршруты мне неизвестно. Можно ли вносить ? Да, модуль проверки пропустит такие маршруты, нужно лишь чтобы длины была не менее, чем у маршрута, уже имеющегося в базе. Нужно ли вносить ? Я не знаю.

02.10.2011 10:29 Наталия
Алексей, что означает ошибка:
502 Bad Gateway
У меня уже однажды была такая ошибка, но тогда я так и не выяснила, что она означает.
Сегодня уже ввела маршруты, всё нормально было. А потом при вводе очередного маршрута выдалась эта ошибка.

02.10.2011 10:31 Наталия
Может быть, эта информация поможет:
перед этим я ошибочно ввела не тот маршрут, он уже есть в БД. Выдалась ошибка, что маршрут уже существует. А после этого стала вводить новый маршрут и вылетела в ошибку 502.

02.10.2011 10:35 Наталия
Попробовала ещё раз после комментариев, и ввелось.
Да, ещё: после того, как выдалось сообщение об уже существующем маршруте, я не смогла удалить путь из окошка. Тут явно где-то застопорилось в программе! Посмотрите, пожалуйста.

02.10.2011 11:05 alexBlack
502 Bad Gateway - браузер получил недопустимый ответ от сервера. У меня тоже изредка бывает. Техподдержка объясняет причину DoS атаками на сервер и приносит извинения за перерывы в работе. Единственый вариант здесь - немного подождать. Будем надеяться, что в дальнешем все наладится.
По поводу \"не смогла удалить путь из окошка\" - это явно проблемы Вашего компьютера или браузера. Серверные скрипты только обрабатывают запрос (грубо говоря строку) и возвращают ответ.

02.10.2011 02:25 Наталия
А нельзя сделать так, чтобы после вывода ошибки о некорректности маршрута поле для ввода очищалось?

02.10.2011 02:26 Наталия
Поле для ввода пути имеется в виду.

02.10.2011 03:29 alexBlack
Я думаю это будет неправильно. Допустим, случайно в поле введен некорректный символ. В этом случае после сообщения об ошибке можно будет исправить введенное значение. А если поле очистить, придется вносить заново и не будет видно в чем была ошибка.

02.10.2011 07:25 Наталия
Да, но у меня после ошибки в поле для ввода уже ничего не удаётся сделать. Просто оно ни на что не реагирует. Даже удалить весь путь не получилось. Вы говорите, что причина в моём компьютере. но я в этом сомневаюсь. Вы попробуйте сами. Введите некорректный маршрут, а после вывода ошибки проверьте поле для ввода.

02.10.2011 07:42 alexBlack
Попробовал, нормально работает. Понимаете, в этом смысле очистка поля ничего не меняет. Обработка полей осуществляется браузером и нет разницы пустое оно или заполненное.

02.10.2011 08:45 Наталия
Сейчас ещё раз попробую ввести существующий маршрут.

02.10.2011 08:51 Наталия
Да, вот сейчас нормально работает. Видимо, в прошлый раз я уже влетела в ошибку сервера, поэтому ничего не могла сделать с полем для ввода.

26.08.2012 04:38 Наталия
Здравствуйте, Алексей!
Почему исчезли некоторые изображения маршрутов?

26.08.2012 11:32 alexBlack
Временные проблемы хостинга.
Не только с изображениями проблема. Иногда вместо странички
появляется сообщение "503 Service Temporarily Unavailable"
Время от времени это у них бывает.

24.11.2013 06:48 Наталия
Алексей, где вы?
Я дала ссылку на БД в дискуссионной группе Al Zimmermann.
Может быть, кто-нибудь заинтересуется задачей и подбросит новые решения :)

31.12.2013 10:53 Наталия
Вот есть же такие идиоты - совать сюда рекламу!
Алексей, закройте эту возможность комментариев. Дайте где-нибудь в уголочке мелким шрифтом ваш контакт. А можно и этого не делать. Кому надо, тот найдёт. С наступающим вас!

05.03.2015 03:27 Bernard Lemaire

I am a French specialist of recreational mathematics . I found 30 years ago : L=212 for the open knight'stour on the 17x17 board, L=500 for 25x25, 906 for 33x33 : send me your email address . here is my email address : bernard.lemaire@cnam.fr Also, my other best tours have the same length as yours but most are different from yours

bernard.lemaire@cnam.fr, so that i can send you these tours

07.03.2015 03:39 alexBlack
Bernard, thank you

13.03.2015 02:40 alexBlack
Coefficient Q added in properties of tours.
Q = L-{(n-3)(m-3)+10} (was proposed by Bernard Lemaire)

26.03.2015 09:49 alexBlack
Наталия, спасибо. Нашел таки ошибку.
Отдельное "спасибо" разработчикам php изменившим кодировку по умолчанию в вызове htmlspecialchars().

26.03.2015 11:35 Наталия
Браво, Бернар!

30.03.2015 10:47 Наталия
Алексей, почему закрытый маршрут 16х16 R. Merson в 172 хода (кажется, совершенно одинаковый) приведён дважды с разными датами?

30.03.2015 11:06 alexBlack
Наталия, спасибо. Исправил.

05.04.2015 12:30 Наталия
Алексей, в списке замкнутых маршрутов на доске 9х9 нет маршрута Bernard Lemaire.

05.04.2015 04:50 alexBlack
В базе он есть, просто отображаются не все маршруты. Там ниже приписка "полный список маршрутов можно посмотреть...". Это ограничение введено чтобы не показывать слишком длинные списки маршрутов. Переместил маршрут на первое место.

05.04.2015 05:51 Наталия
Поняла, Алексей, спасибо. Теперь на первое место претендует моё решение :)

05.04.2015 10:00 alexBlack
done. Пожалуй я увеличу отображаемое количество маршрутов до 20-ти.

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