To demonstrate set union and intersection to her class, Mrs. Putnam asked for three students to each write down a set of numbers.

After they had done so, she looked at their sets and told the class, "the union of these three sets is the first ten counting numbers, but their intersection is empty!"

How many triples (A, B, C) of sets are there such that

A U B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
and
A ∩ B ∩ C = {} ?

(In reply to re(4): Solution FINAL WORD(by Charlie by Charlie)

By the way the program that produced the list is

OPEN "setmeup.txt" FOR OUTPUT AS #2


DATA 1,2,3,12,13,23


FOR i = 1 TO 6


  READ choice$(i)


NEXT


DIM set$(3)





FOR c1 = 1 TO 6


 FOR c2 = 1 TO 6


  FOR c3 = 1 TO 6


   FOR c4 = 1 TO 6


     ERASE set$


     c$ = choice$(c1)


     FOR i = 1 TO LEN(c$)


      set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + "1"


     NEXT


     c$ = choice$(c2)


     FOR i = 1 TO LEN(c$)


      set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + "2"


     NEXT


     c$ = choice$(c3)


     FOR i = 1 TO LEN(c$)


      set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + "3"


     NEXT


     c$ = choice$(c4)


     FOR i = 1 TO LEN(c$)


      set$(VAL(MID$(c$, i, 1))) = set$(VAL(MID$(c$, i, 1))) + "4"


     NEXT


     good = 1


     FOR i = 1 TO 3


       IF set$(i) = "" THEN good = 0


     NEXT


     IF good THEN


       gdCt = gdCt + 1


       PRINT #2, set$(1); " "; set$(2); " "; set$(3); " "


     END IF


   NEXT


  NEXT


 NEXT


NEXT


CLOSE


PRINT gdCt

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Posted by Charlie on 2004-02-10 15:58:42