Sandy Wood
Brain Game: McLanderstone at the Movies
by Sandy Wood - June 1, 2009 - 7:30 AM

THE SOLUTION:

There are 24 possible mixes of products giving a total of 81 possible combinations, as follows:

Don, popcorn – Jon, popcorn – Lon, popcorn – Ron, popcorn
Don, popcorn – Jon, popcorn – Lon, popcorn – Ron, peanuts
Don, popcorn – Jon, popcorn – Lon, popcorn – Ron, nachos
Don, popcorn – Jon, popcorn – Lon, peanuts – Ron, popcorn
Don, popcorn – Jon, popcorn – Lon, peanuts – Ron, peanuts
Don, popcorn – Jon, popcorn – Lon, peanuts – Ron, nachos
Don, popcorn – Jon, popcorn – Lon, nachos – Ron, popcorn
Don, popcorn – Jon, popcorn – Lon, nachos – Ron, peanuts
Don, popcorn – Jon, popcorn – Lon, nachos – Ron, nachos
Don, popcorn – Jon, peanuts – Lon, popcorn – Ron, popcorn
Don, popcorn – Jon, peanuts – Lon, popcorn – Ron, peanuts
Don, popcorn – Jon, peanuts – Lon, popcorn – Ron, nachos
Don, popcorn – Jon, peanuts – Lon, peanuts – Ron, popcorn
Don, popcorn – Jon, peanuts – Lon, peanuts – Ron, peanuts
Don, popcorn – Jon, peanuts – Lon, peanuts – Ron, nachos
Don, popcorn – Jon, peanuts – Lon, nachos – Ron, popcorn
Don, popcorn – Jon, peanuts – Lon, nachos – Ron, peanuts
Don, popcorn – Jon, peanuts – Lon, nachos – Ron, nachos
Don, popcorn – Jon, nachos – Lon, popcorn – Ron, popcorn
Don, popcorn – Jon, nachos – Lon, popcorn – Ron, peanuts
Don, popcorn – Jon, nachos – Lon, popcorn – Ron, nachos
Don, popcorn – Jon, nachos – Lon, peanuts – Ron, popcorn
Don, popcorn – Jon, nachos – Lon, peanuts – Ron, peanuts
Don, popcorn – Jon, nachos – Lon, peanuts – Ron, nachos
Don, popcorn – Jon, nachos – Lon, nachos – Ron, popcorn
Don, popcorn – Jon, nachos – Lon, nachos – Ron, peanuts
Don, popcorn – Jon, nachos – Lon, nachos – Ron, nachos
Don, peanuts – Jon, popcorn – Lon, popcorn – Ron, popcorn
Don, peanuts – Jon, popcorn – Lon, popcorn – Ron, peanuts
Don, peanuts – Jon, popcorn – Lon, popcorn – Ron, nachos
Don, peanuts – Jon, popcorn – Lon, peanuts – Ron, popcorn
Don, peanuts – Jon, popcorn – Lon, peanuts – Ron, peanuts
Don, peanuts – Jon, popcorn – Lon, peanuts – Ron, nachos
Don, peanuts – Jon, popcorn – Lon, nachos – Ron, popcorn
Don, peanuts – Jon, popcorn – Lon, nachos – Ron, peanuts
Don, peanuts – Jon, popcorn – Lon, nachos – Ron, nachos
Don, peanuts – Jon, peanuts – Lon, popcorn – Ron, popcorn
Don, peanuts – Jon, peanuts – Lon, popcorn – Ron, peanuts
Don, peanuts – Jon, peanuts – Lon, popcorn – Ron, nachos
Don, peanuts – Jon, peanuts – Lon, peanuts – Ron, popcorn
Don, peanuts – Jon, peanuts – Lon, peanuts – Ron, peanuts
Don, peanuts – Jon, peanuts – Lon, peanuts – Ron, nachos
Don, peanuts – Jon, peanuts – Lon, nachos – Ron, popcorn
Don, peanuts – Jon, peanuts – Lon, nachos – Ron, peanuts
Don, peanuts – Jon, peanuts – Lon, nachos – Ron, nachos
Don, peanuts – Jon, nachos – Lon, popcorn – Ron, popcorn
Don, peanuts – Jon, nachos – Lon, popcorn – Ron, peanuts
Don, peanuts – Jon, nachos – Lon, popcorn – Ron, nachos
Don, peanuts – Jon, nachos – Lon, peanuts – Ron, popcorn
Don, peanuts – Jon, nachos – Lon, peanuts – Ron, peanuts
Don, peanuts – Jon, nachos – Lon, peanuts – Ron, nachos
Don, peanuts – Jon, nachos – Lon, nachos – Ron, popcorn
Don, peanuts – Jon, nachos – Lon, nachos – Ron, peanuts
Don, peanuts – Jon, nachos – Lon, nachos – Ron, nachos
Don, nachos – Jon, popcorn – Lon, popcorn – Ron, popcorn
Don, nachos – Jon, popcorn – Lon, popcorn – Ron, peanuts
Don, nachos – Jon, popcorn – Lon, popcorn – Ron, nachos
Don, nachos – Jon, popcorn – Lon, peanuts – Ron, popcorn
Don, nachos – Jon, popcorn – Lon, peanuts – Ron, peanuts
Don, nachos – Jon, popcorn – Lon, peanuts – Ron, nachos
Don, nachos – Jon, popcorn – Lon, nachos – Ron, popcorn
Don, nachos – Jon, popcorn – Lon, nachos – Ron, peanuts
Don, nachos – Jon, popcorn – Lon, nachos – Ron, nachos
Don, nachos – Jon, peanuts – Lon, popcorn – Ron, popcorn
Don, nachos – Jon, peanuts – Lon, popcorn – Ron, peanuts
Don, nachos – Jon, peanuts – Lon, popcorn – Ron, nachos
Don, nachos – Jon, peanuts – Lon, peanuts – Ron, popcorn
Don, nachos – Jon, peanuts – Lon, peanuts – Ron, peanuts
Don, nachos – Jon, peanuts – Lon, peanuts – Ron, nachos
Don, nachos – Jon, peanuts – Lon, nachos – Ron, popcorn
Don, nachos – Jon, peanuts – Lon, nachos – Ron, peanuts
Don, nachos – Jon, peanuts – Lon, nachos – Ron, nachos
Don, nachos – Jon, nachos – Lon, popcorn – Ron, popcorn
Don, nachos – Jon, nachos – Lon, popcorn – Ron, peanuts
Don, nachos – Jon, nachos – Lon, popcorn – Ron, nachos
Don, nachos – Jon, nachos – Lon, peanuts – Ron, popcorn
Don, nachos – Jon, nachos – Lon, peanuts – Ron, peanuts
Don, nachos – Jon, nachos – Lon, peanuts – Ron, nachos
Don, nachos – Jon, nachos – Lon, nachos – Ron, popcorn
Don, nachos – Jon, nachos – Lon, nachos – Ron, peanuts
Don, nachos – Jon, nachos – Lon, nachos – Ron, nachos

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Comments (10)

  1. The wording of the question is a bit confusing; I wasn’t sure if you were asking for the number of man-choice combinations, or for the number of combinations of responses (i.e. popcorn-peanuts-nachos-nachos, nachos-nachos-nachos-nachos, etc., disregarding who says what).

    posted by Emily on 6-1-2009 at 8:32 am

  2. I never really thought about it before, but it seems that this can be easily calculated with powers.

    (items)^(number of people)=combinations

    In this case, 3^4=81

    It consistently works with any values. Such as 2 people with 3 items (3^2=9), or 3 people with 2 items (2^3=8), or 8 people with 37 items (37^8=3512479453921).

    posted by Phill on 6-1-2009 at 9:03 am

  3. I’m with Emily. It seems like the question, as worded, is looking for the number of combinations, irrespective of employee.

    posted by Frank on 6-1-2009 at 9:38 am

  4. I understand, Emily… I struggled with the phrasing to get the answer I desired, and actually meant to include both answers in the solution. I’ll go back and add that information.

    Thanks!

    posted by Sandy Wood on 6-1-2009 at 9:46 am

  5. My husbands first response was:

    ONE. Who eats peanuts or nachos at a movie?

    He did then do the math and came up with the correct answer of 81.

    posted by Suzanne on 6-1-2009 at 11:22 am

  6. Nachos seem very popular at theatres today… I see lots of folks with them. Peanuts not so much, but they were common when I was growing up. (Granted, that was in Georgia, which is known for them.)

    posted by Sandy Wood on 6-1-2009 at 12:10 pm

  7. When I can’t remember which should be the exponent I just visualize a key.

    If there are four pins, but only one possible position for each pin then there is only one totals combination 1**4. If one pin has four possible positions then 4**1. So it’s positions (menu items) to the pins (employees) power.

    posted by PartiallyDeflected on 6-1-2009 at 12:53 pm

  8. Come on folks…I know it’s Monday morning but these comments don’t flow with those I’m used to seeing from Floss readers…basic math word problem. Lon = 3, Ron = 3, jon = 3, Don = 3. Multiply and get answer. Order doesn’t matter. :)

    posted by Charlie on 6-1-2009 at 1:15 pm

  9. I agree with the slightly ambiguous wording. I initially got a brain cramp worried about combinations versus permutations, then realized since there were more choosers (4) than choices (3), it couldn’t be permutations (permutations=no repetition, sequence doesn’t matter,like dealing cards from a deck). Number of different person/choice combinations is shamefully easy–3 to the power of 4. Emily’s question about how many different results, ignoring the person/choice pairing, is using combination theory. The answer then becomes (n+k-1)! divided by (k!(n-1)! where n is number of choices and k is number of choosers. That is then 6!/[4!*2!] which works out to 15.

    posted by Chan on 6-1-2009 at 1:24 pm

  10. It’s a combination. 3 possible answers for 4 people. 3^4= 81. Yay, Algebra 2

    posted by Isaac on 6-1-2009 at 3:01 pm

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