#BenEzra: A small Maple package for solving
#the (obvious generalization of the)
#Ben-Ezra riddle: Rabbi Abraham Ben (Ibn) Ezra
#was at sea, when a storm started to rage. 
#There were 15 good guys (Ben Ezra's disciples) 
#and 15 bad guys (empty-minded and naughty (rekim vepokhazim))
#The Captain said that in order to survive, lots should be
#drawn, and 15 passengers should be picked at random to be
#thrown into the sea, in order to ease the ship's load,
#and enable the remaining passenger's to survive.
#The Rabbi replied to the Captain that it was a good idea
#and suggested a pseudo-random protocol for drowning,
#a-la Josephus: eliminate every 9th (when they are placed
#in a circle). This puzzle is mentioned in p. 214
#of the Hebrew Encyclopedia's 
#enrty on `Even Ezra, Rabbi Abraham'. It first appeared
#in Rabbi Moshe Kimkhi's ``Mahalakh Shvilei HaDa'at''
#(c. 1200)
#Written by Doron Zeilberger, Temple University ,zeilberg@math.temple.edu.
#Please report bugs to zeilberg@math.temple.edu
 
 
print(`BenEzra: A small Maple package for solving`):
print(`the (obvious generalization of the)`):
print(`Ben-Ezra riddle: Rabbi Abraham Ben (Ibn) Ezra`):
print(`was at sea, when a storm started to rage. `):
print(`There were 15 good guys (Ben Ezra's disciples) `):
print(` and 15 bad guys (empty-minded and naughty (rekim vepokhazim))`):
print(`The Captain said that in order to survive, lots should be`):
print(`drawn, and 15 passengers should be picked at random to be`):
print(`thrown into the sea, in order to ease the ship's load,`):
print(`and enable the remaining passenger's to survive.`):
print(`The Rabbi replied to the Captain that it was a good idea`):
print(`and suggested a pseudo-random protocol for drowning,`):
print(`a-la Josephus: eliminate every 9th (when they are placed`):
print(`in a circle). This puzzle is mentioned in p. 214`):
print(`of the Hebrew Encyclopedia's `):
print(`enrty on "Even Ezra, Rabbi Abraham". It first appeared`):
print(`in Rabbi Moshe Kimkhi's ``Mahalakh Shvilei HaDa'at''`):
print(`(c. 1200 C.E. )`):
lprint(``):
print(`Written by Doron Zeilberger, `):
print(`Temple University ,zeilberg@math.temple.edu.`):
print(`Please report bugs to zeilberg@math.temple.edu`):
 
 
 print(`First Written: 28 Elul , 5757 `):
 print(`Version of Sept. 30, 1997`):
 print(`written by Doron Zeilberger(zeilberg@math.temple.edu).`):
 print(`" by Doron Zeilberger`):
 print(`The most current version of the package`):
 print(` is  available from`):
 print(`http://www.math.temple.edu/~zeilberg`):
 print(`For a list of the procedures type ezra(), for help with`):
 print(`a specific procedure, type ezra(procedure_name)`):
 print(``):
ezra:=proc()
if args=NULL then
 
print(`BenEzra: A small Maple package for solving`):
print(`the (obvious generalization of the)`):
print(`Ben-Ezra riddle: Rabbi Abraham Ben (Ibn) Ezra`):
print(`was at sea, when a storm started to rage. `):
print(`There were 15 good guys (Ben Ezra's disciples) `):
print(` and 15 bad guys (empty-minded and naughty (rekim vepokhazim))`):
print(`The Captain said that in order to survive, lots should be`):
print(`drawn, and 15 passengers should be picked at random to be`):
print(`thrown into the sea, in order to ease the ship's load,`):
print(`and enable the remaining passenger's to survive.`):
print(`The Rabbi replied to the Captain that it was a good idea`):
print(`and suggested a pseudo-random protocol for drowning,`):
print(`a-la Josephus: eliminate every 9th (when they are placed`):
print(`in a circle). This puzzle is mentioned in p. 214`):
print(`of the Hebrew Encyclopedia's `):
print(`enrty on "Even Ezra, Rabbi Abraham". It first appeared`):
print(`in Rabbi Moshe Kimkhi's ``Mahalakh Shvilei HaDa'at''`):
print(`(c. 1200)`):
lprint(``):
print(`Written by Doron Zeilberger, `):
print(`Temple University ,zeilberg@math.temple.edu.`):
print(`Please report bugs to zeilberg@math.temple.edu`):
 print(`Contains the following procedures:`):
 print(` benezra, RABA  `):
fi:
 
if nops([args])=1 and op(1,[args])=`benezra` then
print(`benezra(r,GoodGuys,BadGuys):`): 
print(`Same as Raba, but instead to the number of good and`):
print(`and bad guys, it inputs lists of them`):
fi:
 
 
if nops([args])=1 and op(1,[args])=`RABA` then
print(`RABA(r,G,B): How to place G good guys (denoted by 1)`):
print(` and B bad guys (denoted by 0) in a line (thought-of as`):
print(` a circle, such that if, starting counting (1) at the first, `):
print(`one throws to the sea the r^(th), and continues until B`):
print(`guys are thrown to see, such that at the end all the`):
print(`bad guys are drownded, and hence all the good guys survive`):
print(``):
print(`For example, to solve the original problem, type`):
print(` RABA(9,15,15) `):
fi:
 
 
 
end:
 
 
T:=proc(resh,m,r)
local n, pl:
 
n:=nops(resh):
 
pl:=(m-1)+r-1 mod n +1:
 
[op(1..pl-1,resh),op(pl+1..nops(resh),resh)],pl,r,op(pl,resh):
 
end:
 
 
 
S:=proc(resh1,pl,r,kha)
local n, m:
 
n:=nops(resh1)+1:
 
m:=((pl-1)-(r-2) ) mod n :
 
if m=0 then
 m:=n:
fi:
 
[op(1..pl-1,resh1),kha,op(pl..nops(resh1),resh1)],m,r:
 
end:
 
benezra:=proc(r,resh,reshNew)
local i,resh1,kha,pl:
 
resh1:=resh:
pl:=1:
 
for i from 1 to  nops(reshNew) do
kha:=op(i,reshNew):
 
resh1:=S(resh1,pl,r,kha):
pl:=resh1[2]:
resh1:=resh1[1]:
od:
 
[op(pl..nops(resh1),resh1),
op(1..pl-1,resh1)]:
 
end:
 
 
RABA:=proc(r,G,B)
local i,resh,reshNew:
 
 
resh:=[seq(1,i=1..G)]:
reshNew:=[seq(0,i=1..B)]:
benezra(r, resh,reshNew):
end: