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Trading cards (Posted on 2002-05-03) Difficulty: 3 of 5
A trading card series has 200 different cards in it, which are sold in 5-card packages.

Each package has a random sampling of the cards (assume that any card of the 200 has an equal chance of being in a package).

On the average, how many packages will need to be bought to collect the complete series if...

  • A: all the cards in a package will always be different
  • B: a package can have repeats

  • See The Solution Submitted by levik    
    Rating: 4.1818 (11 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    re(3): Simulation results | Comment 21 of 36 |
    (In reply to re(2): Simulation results by Tony)

    I've corrected a couple of typos (pack vs packet for the array name, packCnt vs packetCnt for the iteration variable/subscript) so it looks like
    RANDOMIZE TIMER
    tot = 0: totI = 0
    DO
    REDIM c(200)
    ct = 0: ctr = 0
    DO
    REDIM packet(5) 'Individual pack
    FOR packetCnt = 1 TO 5
    r = INT(RND(1) * 200 + 1)
    packet(packetCnt) = r ' fill in each card in the pack
    NEXT
    FOR packetCnt = 1 TO 5 ' see if we already have a card (but this doesn't check from the pack)
    r = packet(packetCnt)
    IF c(r) = 0 THEN
    c(r) = 1
    ct = ct + 1 ' ct must get to 200 each trial
    END IF
    NEXT
    ctr = ctr + 1 ' ctr is number of purchases for a complete set
    IF ct = 200 THEN EXIT DO
    LOOP
    totI = totI + ctr ' Number of packs
    numTry = numTry + 1
    PRINT numTry, ctr, totI / numTry
    LOOP
    but this still does not have a check for non-duplication within packet. The 3085th line is
    3085 296 233.7284
    for an average of 234 packets per trial.


      Posted by Charlie on 2003-01-29 17:00:45

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