Apparent Bug In "Permutations" Function In Maxima 5.9.3

Mark Lawton · science forum beginner Joined: 22 Mar 2006 Posts: 11

I was investigating the following question: "In my class, there are 99
students other than me. 50 of us play soccer, 45 basketball and 50 play
volleyball. Only 15 of us play all three games. Everyone plays at least
one game. How many play only two games?"

I wrote a Maxima program, but its output was the error message, "part
fell off end".

A bit of debugging yielded the fact that the "permutations" function is
altering variables that it shouldn't. Closing and restarting Maxima
makes no difference.

In the code, the following 2 lines have been added for debugging:

if length(part(soccer,1)) = 2 then print(1)
if length(part(soccer,1)) = 2 then print(2)

The fact that when the code runs, 2 is printed before 1 seems to show
that the statement socPerm: permutations(soccerSet) is illegally
altering the value of the variable "soccer".

Here is the code:

(soccer: integer_partitions(35,3),
baseball: integer_partitions(35,3),
volleyball: integer_partitions(30,3),
listintersect(list1, list2) := intersect(setify(list1), setify(list2)),
for soccerSet in soccer do
for baseSet in baseball do
if cardinality(listintersect(soccerSet, baseSet)) > 0 then
for volleySet in volleyball do
if cardinality(listintersect(soccerSet, volleySet)) > 0 and
cardinality(listintersect(baseSet, volleySet)) > 0 then
(if length(part(soccer,1)) = 2 then print(1),
socPerm: permutations(soccerSet),
if length(part(soccer,1)) = 2 then print(2),
basPerm: permutations(baseSet),
volPerm: permutations(volleySet),
for socSoln in socPerm do
for basSoln in basPerm do
if part(socSoln,1) = part(basSoln,1) then
for volSoln in volPerm do
if part(socSoln,2) = part(volSoln,1) and part(volSoln,2) =
part(basSoln,2) then
(soc: part(socSoln,3),
socBas: part(socSoln,1),
socVol: part(socSoln,3),
bas: part(basSoln, 3),
basVol: part(basSoln,2),
vol: part(volSoln,3),
twoGames: socBas + socVol + basVol,
print("Soc",soc,", bas",bas,", vol",vol,",
soc&bas",socBas,", soc&vol",socVol,", bas&vol",basVol,", two
games",twoGames))))$

GLaight@googlemail.com · science forum beginner Joined: 15 Jul 2006 Posts: 1

Off topic to the apparent bug - but I ran a different program and found
the solution (warning - this took over 2 hours to run on my PC):

(solns: set(),
test: integer_partitions(100,7),
for lists in test do
if member(15, lists) then
(perms: permutations(lists),
for sector in perms do
if part(sector, 5) = 15 then
(soc: part(sector,1) + part(sector,2) + part(sector,4) + 15,
bas: part(sector,2) + part(sector,3) + part(sector,6) + 15,
vol: part(sector,4) + part(sector,6) + part(sector,7) + 15,
if soc = 50 and bas = 50 and vol = 45 then
solns: adjoin(sector, solns))))$

After running this, the cardinality of the "solns" solution set was 136
- so I ran another program:

for soln in solns do
print("Soc",soln[1],", Bas",soln[3],", Vol",soln[7],",
soc+Bas",soln[2],", soc+Vol",
soln[4],", Bas+Vol",soln[6],", Total two-sports", soln[2] + soln[4] +
soln[6])$

The output confirmed that there was always a total of 15 people doing 2
sports.

robert.dodier@gmail.com · science forum beginner Joined: 02 Oct 2005 Posts: 26

Mark Lawton wrote:

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