A few days ago (Tuesday 21 October) marked 100 years since the birth of Martin Gardner, one of the most influential American mathematics and science writers of the 20th century. Gardner was an extraordinarily prolific writer and correspondent in mathematics, science, religion & philosophy having authored or edited over 100 books - not to mention countless articles and reviews - with his first book published in 1936 and the last in 2010, the year of his death at the age of 95.

Gardner's contributed hugely to recreational mathematics (see my recreational mathematics bibliography). My first encounter with anything written by Gardner was a set of two books that my mother gave to me when I started teaching mathematics in 1983. They were aha! Insight (1978) and aha! Gotcha: Paradoxes to Puzzle and Delight (1982). They are absolutely delightful books that I found personally entertaining and enlightening - and which also provided me with some good material for my teaching. Here is my favorite problem from aha! Insight entitled One Too Many that I've often used with students to get them thinking about important number concepts such as factors, multiples, divisibility and least common multiples.

Many non-Americans may not be familiar with marching bands and the number of members expected to be in an average marching band.  Of the possible answers 25, 85, 145, etc, I think that 85 is the best answer since 25 would be a bit small for a marching band and 145 is too large.

A nice variant of this problem (presented in the book in the discussion section after the problem) is to consider when a band marches by in rows of 2, 3 and 4 the last row has one too few. Then the answer is the sequence of numbers that are one less than a multiple of 12 and divisible by 5, i.e. 35, 95, 155, etc.  Also presented is a similar, but challenging, problem posed by American puzzle make Sam Loyd (1841-1911) that describes a band marching by in rows of 10, 9, 8, 7, 6, 5, 4, 3 and 2 but every time the last row is missing one person (one too few). In desperation the band director has the band march in a single file. Assuming the band has less than 5000 members, how many were in the band? Instead of a LCM of 12 as in the previous two problems, the LCM is 2520 - so there 2519 people in the band. However, in my mind, 2519 is too many for a marching band and might be more appropriate for a group of marching soldiers. There are a few other similar challenging problems presented in the discussion section.

I highly recommend including both books in your collection of teaching resources - and in your personal library.