## Math Tutoring Service

See my Mathematics Tutoring Service on Thumbtack

### Coded arithmetic puzzles

In a course I am developing, I want to give out some math problems for people to work on that should be in the grasp of adults without much math background at all. One such problem is what I call "coded arithmetic puzzles". The commonest example I know is "Send More Money": Solve S E N D + M O R E = M O N E Y, where each of the 8 different letters in the equation represents a different digit.

I would like to find a collection of these types of puzzles that would enable me to give different classes different puzzles. The puzzles should not be too tedious and should not require too much cleverness; in other words of the difficulty of Send More Money, or easier. Perhaps someone has written a program that would generate puzzles of this sort.

Does anyone know if there is a formal name for this type of problem? "Coded arithmetic puzzles" is not a very helpful Google search.

### Name Change

Cambridge Math Learning, Inc. is now doing business as Math for the Rest of Us. I think this emphasizes the mission of the company, which is to teach mathematics to the "bottom 80%" of adult math learners; those who have been poorly served by mathematics instruction in the past and most of whom now have anxiety when facing mathematics that they must learn.

### More on Ordering a Multiset

I posed problem A3, to find a formula for the k-th largest element of an n-element multiset A. I found a very interesting formula that is unknown to several famous combinatorists, including Donald Knuth, and I have submitted a problem to the MAA Monthly Problems section which asks for the solution that I found, a linear combination of certain symmetric functions. However, Knuth told me that there is a simpler known formula of a different type. Knuth's formula is

min(maxk)

where (maxk) is a set of C(n,k) numbers, each of which is the maximum of a different subset of A of size k.

Pretty cute!