Harry Kaplan joins us for discussion of cake and coffee– and leaves us with a counter-intuitive puzzle…
Archive for math puzzles
A quick hello from Chaim and Kyle as the Math Factor returns!
We’ll be the first to say our Coffee Pot Question isn’t our deepest puzzle ever, but it sure did make a difference in Chaim’s life!
When I became chairman of my department a few years ago, I moved from my office far down at the end of the hall to one much closer to the center of action: the tea room! I make a lot more visits there than I used to, and began to notice a frustrating pattern:
Far more often than seems reasonable, there’s not even a full cup of coffee in the coffee pot! Once again, someone has left a nearly empty pot with no regard to the next person (me, whine)!
This seems to happen so often I began to wonder what kind of boors I’ve been working with all these years. They seem like nice people and all, but…?
And then I realized: there’s a perfectly logical reason, a mathfactor puzzle, if you will, that explains this phenomenon perfectly, no boors required, no special tricks, just sensible activity by all. My faith in my colleagues has been restored.
Why is it that on average I see an emptier rather than fuller coffee pot?
It’s been a while since I posted a puzzle and happened upon a nice one today.
You find yourself babysitting a friend’s marble collection while he’s away at a conference of collectors. The housekeeper, being an honest type, admits to having disturbed one of the displays. She assures you that she returned all the marbles and shows you ten marbles laid out thus:
* * * * *
* * * * *
That looks fine, but the note to the side of it says five lines of four marbles each. Since this is two lines of five marbles, must there be marbles missing or can they be laid out in a manner consistent with the note?
In Golden Earring – Radar Love I had a big problem.
This the solution so please read the problem first and have a go at solving it yourself.
My wife has lost a golden earring, I can buy a bunch of similar earrings but I know one is a fake.
I can weigh two groups of earrings, each weighing can give one of three results: they weigh the same; the left group is heavier, the right group is heavier.
The question is – how many earrings can be in the bunch I buy and leave me confident that I can find the fake with just three weighings?
In this special segment, John H. Conway reminisces on his long friendship and collaboration with Martin Gardner.
Greg Chaitin, author most recently of MetaMath!, discusses the ubiquity of undecidability: incredibly all kinds of mathematical and physical systems exhibit utterly unpredictable, baffling behavior– and it’s possible to prove we can never fully understand why!
You and other party-goers are lead to different places in a wood blind-folded. You’re instructed to remove your blindfold at the sound of a horn and read a letter you’ve been provided. When the bell sounds, you remove the blindfold and the letter reads thus:
You’ll notice around you that there are lengths of rope tied between hundreds of trees around you. You may notice that any tree with any rope tied to it has exactly two ends tied to it, each stretching to a different tree. In fact, these hundreds of treees form a giant concave polygon. Some of you are inside that polyon and others are outside. To win the game, you must be the first to reach the clubhouse at the top of the hill (which is outside of the polygon!) and report correctly whether you were initially inside the polygon or outside of it. You can pass under the ropes, but please don’t change them in any way. Good luck!
What strategy might you employ to determine your status and require as little time as possible to get back to the clubhouse?
The world’s largest ever exhibit of Escher’s works is on display, right now, at the Boca Raton Musuem of Art If you can, this is a must see event! We talk with the collector, Rock J. Walker about his fascination with this amazing work.
And of course we answer last week’s puzzle, and hear from listeners!
A bit lazy, but we’re pretty far behind. Herewith, are
GQ: Durned Ants
GR: VIth Anniversary Special
GS: I Met a Man