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Mensa = Smart?

One of my coworkers has a page a day mensa calendar. As he solves the puzzles he gives them to me. Most are straight forward, but he showed me a very interesting one yesterday.

Kim has three vases in her living room, each containing the same number of flowers. Kim adds three fresh flowers to one vase, which now has two more than the new average. How many flowers were in the vases originally?

See my comments (to my own post) for the answer if you need it.

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( 4 comments — Leave a comment )
grieve
Oct. 4th, 2006 02:11 pm (UTC)
Solution
It turns out that any non-negative integer works. They give the answer as 6 oddly enough (or is that evenly enough?).

For a pseudo rigorous proof:
X is the original number of flowers per vase. So the old average of flowers per vase is (3X)/3, which of course just simplifies to X. The new average is (3X + 3)/3, which simplifies to X + 1.

The amount of flowers is the new vase is X + 3

So (X + 3) - (X + 1) = 2 for any non-negative X.

Obviously Mensa is not proof reading their puzzles. I guess they are smart, but lazy.

Additionally if you have N vases and all with the same amount of flowers, and Add N Flowers to one of the vases the difference in the new average and the number of flowers in the new vase will be N - 1.

Let Y be the number of flowers per vase.

The old average is NY/N which simplifies to Y.

The new average is (NY + N)/N which simplifies to Y + 1.

The new amount of flowers is Y + N.

So the difference of the new flowers and new average is Y + N - (Y + 1)

Simplifying to N - 1.


chikuru
Oct. 4th, 2006 09:41 pm (UTC)
Re: Solution
It works for negative numbers of flowers too.
grieve
Oct. 4th, 2006 10:04 pm (UTC)
Re: Solution
Mathematically you are correct, but I was trying to maintain the physical constraints, and I have never seen a negative flower. :)
(Anonymous)
Feb. 27th, 2007 06:09 am (UTC)
Re: Solution
The problem says "added fresh flowers". I would count a negative number as "dead" flowers.

Still a solution.

Thierry
( 4 comments — Leave a comment )

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