Impossible? Try anyway!
(An archive question of the week) Here’s a little problem with some big lessons for problem solving.
Bayes and Virus Testing
News about testing for viruses has reminded me of a couple problems that I linked to some time ago, but never dealt with directly. The question is, given data such as the result of a (fallible) blood or swab test, how sure can we be of the results? The answer is sometimes surprising.
Invariants for a State Machine
(A new question of the week) Although we focus in this blog on questions at early college level and below, we do get questions at higher levels. This one deals with finding an invariant for a finite state machine, with possible movements of a robot as the example.
Logic Puzzles: Who Owns the Fish?
Having looked at methods for solving four logic puzzles, I’ll close the series with a classic, this one involving five houses, five colors, five countries, five drinks, five cigarettes, and five pets – that’s six attributes to juggle! (Last time, we had only 3 or 5.) Once again, the challenge is to solve it without …
Logic Puzzles: Five Murders, Five Friends
Here are two more logic puzzles similar to those we looked at last time. Each is partly solved, enough to teach how to approach such problems (this time, using tables), but leaving enough of a challenge for you to finish up. What’s new here is that we will be using tables to keep track of …
Logic Puzzles: Five Jars, Five Teams
We have received a number of questions about various kinds of logic puzzles. This week I want to collect several for which we gave hints or partial solutions that demonstrate in detail how to think, without taking away all the fun. These all involve a set of people or objects that have a set of …
“Order of Operations” Puzzles
We have often received questions about things called “Order of Operations problems”, or some similar name. Generally, what that means is simply that they are puzzles to give lots of practice evaluating expressions using the order of operations. I have collected a few quite different puzzles in this broad category.
The 24 Game and Kin
We are looking at various mathematical puzzles and games, with a focus on discussing rules and strategies, and then letting you play. Last time we discussed Four Fours, in which we are given a fixed set of “inputs” to a calculation (usually 4, 4, 4, 4), and want to find expressions that yield as many …
Four Fours and Friends
This has been a good time for doing puzzles to stay busy (as a family, or a class, or as distanced friends, for instance). The next few posts will present various mathematical puzzles and games you might enjoy. Although often when a problem I quote was originally left unsolved, I have filled in the gap …
John Conway on Thinking and Teaching
(An archive question of the week) When I heard Thursday that the great mathematician John Conway had died (see the New York Times obituary here), I recalled not only his books I have read, but his involvement in Ask Dr. Math‘s early days. In addition to a couple dozen quotes from him, there were several …