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(Cue organ music.) We return to the local accounting firm of McLanderstone & Associates. The old man’s four key employees, Lon, Ron, Jon, and Don, are in their respective offices, trying to make it through another Monday. McLanderstone will sometimes ask the quartet’s opinions on seemingly banal subjects, just to get their minds “in gear” to begin the long workweek. This morning, he dropped an inter-office instant message to the four, which asked: “Which is better at a movie theatre: popcorn, peanuts, or nachos?” Today’s Brain Game:
Provided that each man did respond with his choice,
how many different possible combinations of answers
could McLanderstone receive from the four men?
Comments (10)
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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
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
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
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
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
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
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
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
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
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