 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Set Me Up (Posted on 2004-02-10) 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 = {} ?

 See The Solution Submitted by DJ Rating: 4.3636 (11 votes) Comments: ( Back to comment list | You must be logged in to post comments.) re(5): Solution FINAL WORD(by Charlie | Comment 29 of 31 | (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

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 Please log in:

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