Tuesday, November 21, 2006

The beagle boys

In the cartoon show, Duck Tales (and in the comics), the beagle boys always had the numbers 167 used in two different sequences on their shirts to indicate their prison number. For instance, one beagle boy had the number 167 671, while another had 761 716. The only restriction was the pattern could not be repeated, so the number 167 167 would not be possible. How many different combinations could they have and still be unique?

In other words, how many beagle boys could there be?

10 comments:

  1. This is a factorial:

    3! = 6

    ReplyDelete
  2. Not sure I understand Mr. Don's answer. Seems to me that for each 3-number sequence, there are 6 possibilities (which is 3 factorial), and then that there are 30 total possible combinations where the second sequence isn't the same as the first. In other words, the first one can be any of the six possibilities, and the second one can be any of the remaining 5, and 6 * 5 = 30.

    ReplyDelete
  3. Andy,

    I may have mis-read the question becuase of the spaces Mike has between the numbers: 167 671 is really 167671, so my answer does not make sense. Sorry about that.

    So we have a six-digit number that has three different integers of which only two of each integer can appear.

    The second restriction is that the number cannot be reptitive, eg. 761761.

    That will take a little more head scratching on my part.

    ReplyDelete
  4. Yes, I agree with andy.

    Two pais of 3! is 6x6=36, minus the 6 numbers that will be repetitive leaves 30.

    ReplyDelete
  5. There are 6 ways to rearrange 761:

    167, 176
    617, 671
    716, 761

    Pick one of them for the left group, (6 choices), pick a different for the right group (from the 5 left)

    6*5 is 30

    ReplyDelete
  6. I think you all have explained it every way that it can be done. 30 it is.

    BTW, I have noticed (we have it on DVD) that a 4 creeps in to the sequence every once in a while.

    ReplyDelete
  7. I hope you have kids, Mike, and that the DVDs aren't just for you and your partner. :)

    ReplyDelete
  8. Does it matter that we bought (season 1) before we had kids?

    :-)

    ReplyDelete
  9. 15

    167 176
    671 617
    716 761

    3*3= 15

    ReplyDelete

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