[math-fun] Name of board game
There was a board game played (I think) on a 5 by 5 board. Each player had 4 blots which they alternately placed on empty squares on the board. After all pieces were placed, players alternately moved one piece as a king in chess, to an empty square. The object was to be first to form either a straight line of four adjacent blots, horizontally, vertically, or diagonally, or place the blots at the corners of a square. I seem to think it was called "teco" or something similar.
Hello Math-Fun, I'm looking for loops with the hereunder rules: -start with a(1) -if a substring of a(1) is made of identical digits, replace the said substring with the sum of its digits -iterate until there are no more substrings with identical digits in a(1) -double a(1) and start the pro- cedure again. Ex. a(1)= 55027771 a(1)=1002211 a(1)=1042 a(2)=2084 a(3)=4168 a(4)=8336 a(4)=866 a(4)=812 a(5)=1624 etc. 18 enters in the loop 18-36-72-144-(18) Best, É.
If I understand you correctly, you are defining a function C(n) (c stands for "collapse"), which replaces runs of consecutive identical digits by their sum; then you define D(n) as n (if n == C(n)) and D(C(n)) otherwise -- in other words, keep applying C until the result stops changing. Your overall question is about the dynamics of E(n) = D(2n). If that's correct, then I think 178 is the smallest element of a 24-step loop. I did that by hand. For some reason I keep making stupid mistakes trying to code this. On Tue, Jun 5, 2012 at 3:50 AM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
Hello Math-Fun, I'm looking for loops with the hereunder rules: -start with a(1) -if a substring of a(1) is made of identical digits, replace the said substring with the sum of its digits -iterate until there are no more substrings with identical digits in a(1) -double a(1) and start the pro- cedure again.
Ex. a(1)= 55027771 a(1)=1002211 a(1)=1042 a(2)=2084 a(3)=4168 a(4)=8336 a(4)=866 a(4)=812 a(5)=1624 etc.
18 enters in the loop 18-36-72-144-(18) Best, É.
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Eric Angelini:
18 enters in the loop 18-36-72-144-(18)
A small quibble: Since the doubling appears to be part of "the procedure", I make that: 18, 36, 72, 144, 36, ..., so I would represent the loop portion as {36, 72, 144}, putting the smallest member of the loop first. There are loop members, and loop precursors that run into loops, and I take 18 as one of the latter. Trivially, I think we can add a zero to the end of each member of a loop to turn it a new loop; for example, {360, 720, 1440}. So far, I have nine non-trivial loops (assuming that I have done things correctly) and put them here: http://chesswanks.com/num/iterate(2*iterate(SumAdjacentIdenticalDigits)).txt They are introduced by [smallest precursor, loop length]. Additionally, I have marked the largest loop member with an asterisk. Allan Wechsler:
I think 178 is the smallest element of a 24-step loop.
Except for my quibble, yes.
Thank you, Allan and Hans! Quibble is right, I think! Best, E. Envoyé d'un aPhone Le 5 juin 2012 à 21:51, "Hans Havermann" <gladhobo@teksavvy.com> a écrit :
Eric Angelini:
18 enters in the loop 18-36-72-144-(18)
A small quibble: Since the doubling appears to be part of "the procedure", I make that: 18, 36, 72, 144, 36, ..., so I would represent the loop portion as {36, 72, 144}, putting the smallest member of the loop first. There are loop members, and loop precursors that run into loops, and I take 18 as one of the latter.
Trivially, I think we can add a zero to the end of each member of a loop to turn it a new loop; for example, {360, 720, 1440}.
So far, I have nine non-trivial loops (assuming that I have done things correctly) and put them here:
http://chesswanks.com/num/iterate(2*iterate(SumAdjacentIdenticalDigits)).txt
They are introduced by [smallest precursor, loop length]. Additionally, I have marked the largest loop member with an asterisk.
Allan Wechsler:
I think 178 is the smallest element of a 24-step loop.
Except for my quibble, yes.
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The loops of Hans are also here now: http://www.cetteadressecomportecinquantesignes.com/Collapse.htm Many thanks again to all. É.
On Tuesday 05 June 2012 03:59:52 Dave Dyer wrote:
Teeko
One of the few board games to be the subject of an opera: http://www.quinapalus.com/musical.html (Though it's only about 10 minutes long, and it's as much making fun of Scarne's self-promotion as it is about the game.) -- g
participants (6)
-
Allan Wechsler -
Dave Dyer -
David Wilson -
Eric Angelini -
Gareth McCaughan -
Hans Havermann