As an aside: I feel like I'm on a blog post marathon. I don't intend to keep posting things so close together, but I keep finding something new I want to post! Thankfully, my recent posts have been quick and easy to write - with a huge exception to my Under Grace, Part III post - so it hasn't eaten away my time. I'm not intending to keep up this rapid posting schedule indefinitely, in case anyone is wondering :). This weekend should be slow while I'm out of town.
As one of my math education electives in college, I took a problem-solving course. It would have proved to be my favorite course in college had it been structured differently, but regardless, I loved working through different problem types and tweaking my thoughts until I reached a solution. It was pure fun. I kept my course folder for memories and to occasionally pull from for the classes I teach.
We had some extra time in geometry yesterday so we did some problem-solving exercises from the back of the book that were similar to the ones I did in my problem-solving course. They loved them! Of course, who wouldn't? It's like working a puzzle :). As part of the homework assignment, I told my students I would e-mail them a few problems from my folder. They're just so much fun, I thought I'd share them here, along with a bonus problem just for all of you. For a treasure trove of such problems, try my former professor's website. That should keep you busy for about a decade :).
Feel free to comment with answers. If you want to work the problems out on your own, don't look at the comments first! I'm especially interested to see if anyone can get the last one. The first ones are quite doable, but the last requires a bit more.
What Color is my Hat?
Three people are sitting in a row, one behind the other, facing forward. The third person can see the two people in front of him, the second person can see the person in front of him, and the first person can see no one.
There are 5 hats: 3 red hats and 2 black hats. A 4th person places one hat on each of the three people's heads without each person knowing his own hat color.
The 3rd person says, "I cannot tell what color hat I have."
The 2nd person says, "I cannot tell what color hat I have."
The 1st person says, "I know for sure what color hat I have."
Is he telling the truth, and if so, what color hat does he have?
Crime and Logic
Four suspects of a crime made the following statements to the police:
Andy: Carl did it.
Bob: I did not do it.
Carl: Dave did it.
Dave: Carl lied when he said I did it.
Given that one of them "did it" and that exactly one of them told the truth, who did it?
Secret Whole Number
By using the answers to the following questions, Patrick determines Sam's secret whole number.
(1) Is it a factor of 30? --> yes
(2) Is it a prime number? --> no
(3) Is it a multiple of 3? --> no
(4) Is it less than 3? --> no
What is Sam's secret number?
And just for my blog readers, here's a bonus problem! This was my favorite problem that I did in college, I think.
I'll bake chocolate chip cookies for anyone who figures this problem out correctly. (A coconut dessert would be more appropriate, but I don't cook with coconut.) The cookies are available for pickup at our home in Metro Atlanta :). And no doing a search on the internet for this problem; your solution has to be your own work. Happy problem solving!
The Coconut Problem
On a desert island, 5 men and a monkey gather coconuts all day. At nighfall the men go to sleep, leaving the monkey to guard the stash.
The first man wakes up during the night. He divides the stash into 5 equal shares and gives the remaining coconut to the monkey. He takes his share and puts the remaining 4 shares back together in a pile.
The 2nd, 3rd, 4th, and 5th men each wake up separately in succession throughout the night and do the same as the 1st man, each unbeknownst to the others; they each divide the (remaining) pile of coconuts into 5 shares, giving the extra coconut to the monkey, take their share and return the rest of the coconuts to a big pile.
When they all awaken in the morning, the pile is a multiple of 5 coconuts. What is the minimum number of coconuts originally present?