Joho the Blog
An Entry from the Archives

I was going to take a knife and cut through the deck, chopping every card in half. That would give me two decks with exactly the same number of up and down cards!

Her answer is better :-)

took me a minute...
count out ten and turn them over?
If none... 10 vs. 10
If one... 9 vs. 9
etc.

thought n thought---didnt work even reading answer, so googled you this am and thanks to you-all i got it. very clever (or im not, but anyway) thanks for posting it, ill sleep a little better tonight. btw-i sent your version to a number of people, so you're famous--billr

{Spoiler?}

The parity answer is indeed clever. What interests me is the implicit assumptions we do and don't make. In this case the notion that two piles mean two even piles. Turning over the cards is also questionable but I'll grant that since thinking of flipping the cards by itself is not the answer without seeing the parity solution.

Strange timing -- I found this because I was looking for her column online for the 28th (today) where she correctly points out that students blame themselves for not understanding a teacher when it is really the teacher's failure.

Overall, I do confess to reading Parade along with the comics in the Globe. Her columns do have some insights but also some big misses that are the flip side of the card problem -- it's a question of which implicit assumptions are real constraints and which are self-imposed.

This week I can't help but observe that trying to coin a word for www. as dubdot is wrong -- it sexdot by that reasoning - three double u's is a sextuple u. But then the column is not very web savvy -- it's a generational thing.

While Marilyn's overall intelligence is, in a word, incredible, the difficulty of this problem is not. A similar form of this problem appeared recently in a competition called "Tournament of Towns" which is held in Russia or some part of Europe (sorry I don't remember exactly). The problem involved a million coins with 32 of them face up in the dark. It was an Easy or Junior level question, meaning it was given to 9th and 10th graders. This problem is but a simple example of basic mathematical parity and logic. Take a look at some of the solutions to high school olympiad mathematics problems. There you will find true cleverness.

http://www.hyperorg.com/blogger/mtarchive/002022.html

turn on a light.