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February 2020 - Challenge
In the famous Snakes and Ladders game, there is a board with 100 squares. You start at square 0 (just outside of the board) and then proceed to advance based on your move, which is dictacted by the throw of a fair dice. If your piece lands on a square that is at the very bottom of a ladder, you climb it. If your turn lands you at the head of a snake, you slide down to the bottom of its tail. And if your turn takes you out of the board (a square > 100), you stay in the square where you are at the time the dice was thrown.
Your challenge this month is to design a game with 10 ladders and snakes altogether that will lead to an expected number of moves (rounded to the 6th decimal place) of 66.978705.
Provide your answer as a list of 10 [source,target] pairs.
As an example, the standard game of 19, with 9 ladders and 10 snakes:
[1,38],[4,14],[9,31],[21,42],[28,84],[36,44],[51,67],[71,91],[80,100],[16,6],[47,26],[49,11],[56,53],[62,19],[64,60,],[87,24],[93,73],[95,75],[98,78] has an expected 39.225122 moves (again, rounded to the 6th decimal place).
Bonus '*' for getting to at least 12 digits after the decimal point to 66.978705007555420778.
We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!
We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com
Challenge:
28/01/2020 @ 12:00 PM EST
Solution:
03/03/2020 @ 12:00 PM EST
List Updated:
03/03/2020 @ 12:00 PM EST
People who answered correctly:
Guillermo Wildschut (28/01/2020 10:29 AM IDT)
Anders Kaseorg (28/01/2020 11:31 AM IDT)
*Bert Dobbelaere (28/01/2020 11:38 PM IDT)
Alper Halbutogullari (28/01/2020 11:38 PM IDT)
David Greer (30/01/2020 02:00 AM IDT)
Daniel Chong Jyh Tar (30/01/2020 11:37 AM IDT)
Lorenzo Gianferrari Pini (30/01/2020 01:09 PM IDT)
Pern Jie Quah (31/01/2020 02:16 AM IDT)
Todd Will (31/01/2020 06:30 PM IDT)
Lorenz Reichel (31/01/2020 09:31 PM IDT)
Willem H Hendriks (01/02/2020 12:29 AM IDT)
Gary M. Gerken (01/02/2020 07:15 AM IDT)
Harald Bögeholz (02/02/2020 09:00 AM IDT)
Chris Marks (01/02/2020 09:10 PM IDT)
Joerg Schepers (03/02/2020 12:28 AM IDT)
David Friedman (03/02/2020 08:29 PM IDT)
Dominik Reichl (03/02/2020 09:03 PM IDT)
Dieter Beckerle (04/02/2020 12:55 AM IDT)
Sebastian Bohm & Martí Bosch (04/02/2020 03:57 PM IDT)
Mateus Siqueira (04/02/2020 04:10 PM IDT)
Leonardo Joau (04/02/2020 04:57 PM IDT)
Kevin Naslund (04/02/2020 05:35 PM IDT)
*Asaf Zimmerman (04/02/2020 11:34 PM IDT)
Ayush Jain (05/02/2020 09:51 AM IDT)
Kang Jin Cho (05/02/2020 10:22 AM IDT)
Greg Janée (05/02/2020 02:32 PM IDT)
Khaled Fayed (05/02/2020 02:41 PM IDT)
Rob Pratt (08/02/2020 01:09 AM IDT)
Andrew Mullins (08/02/2020 10:31 PM IDT)
Shouky Dan & Tamir Ganor (09/02/2020 09:00 AM IDT)
Andreas Stiller (09/02/2020 06:21 PM IDT)
David Krief (10/02/2020 03:03 PM IDT)
Andreas Puccio (10/02/2020 08:31 PM IDT)
Peter Huggins (10/02/2020 10:21 PM IDT)
Stephen Barr (11/02/2020 05:51 AM IDT)
Tyler Mullen (11/02/2020 08:26 AM IDT)
Arthur Vause (11/02/2020 06:41 PM IDT)
Vladimir Volevich (14/02/2020 05:18 PM IDT)
Yusuf AttarBashi (15/02/2020 09:40 PM IDT)
Jack Kennedy (16/02/2020 04:43 PM IDT)
Nik Vlachos (19/02/2020 12:40 AM IDT)
Thomas Huet (19/02/2020 08:31 PM IDT)
Alexander Strasser (21/02/2020 01:48 PM IDT)
Dimas Ramos (22/02/2020 06:07 PM IDT)
Stanislav Grudnitskiy (22/02/2020 08:57 PM IDT)
Graham Hemsley (23/02/2020 07:24 PM IDT)
Peter Gerritson (23/02/2020 09:22 PM IDT)
Dipto Thakurta Dipto Thakurta (24/02/2020 06:39 AM IDT)
Diana Gornea (24/02/2020 11:23 AM IDT)
*Latchezar Christov (24/02/2020 03:27 PM IDT)
JJ Rabeyrin (24/02/2020 11:13 PM IDT)
Daniel Bitin (25/02/2020 12:15 AM IDT)
Kai Guttmann (25/02/2020 07:06 PM IDT)
Nyles Heise (26/02/2020 05:08 AM IDT)
Jean Bertrand Gauthier (26/02/2020 12:24 PM IDT)
Hugo Pfoertner (26/02/2020 01:22 PM IDT)
*Bertram Felgenhauer (27/02/2020 11:21 AM IDT)
Kottmann Markus (27/02/2020 10:37 PM IDT)
Robert Lang (28/02/2020 12:02 PM IDT)
Stéphane Higueret (28/02/2020 01:42 PM IDT)
Govind Jujare (28/02/2020 07:13 PM IDT)
Radu-Alexandru Todor (01/03/20 12:57 AM IDT)
Collin Pearce (01/03/20 08:11 AM IDT)
Marco Bellocchi (01/03/20 09:02 AM IDT)
Jonah Mann & Joe Hooker (01/03/20 11:44 AM IDT)
Muralidhar Seshadri (01/03/2020 06:06 PM IDT)
Erik Wünstel (01/03/2020 06:35 PM IDT)
Calvin Pozderac (01/03/2020 07:17 PM IDT)
Oleg Vlasii (01/03/2020 11:15 PM IDT)
Eden Saig (02/03/2020 01:41 AM IDT)
Li Li (02/03/2020 06:38 AM IDT)
Florian Fischer (03/03/2020 07:52 AM IDT)