Michael Maynard from Wellington, who must be the leading compiler of additive alphametics in New Zealand, wrote to me to share some of his ideas.

Alphametics, you may remember [Neurobics: September 1996], are a type of puzzle in which digits in an arithmetical calculation are replaced by letters of the alphabet. Good alphametics not only have a single solution but make up a sensible phrase. An example is SEND + MORE = MONEY with solution 9567 + 1085 = 10652.

Michael suggests that the best alphametics should not only make sense but contain exactly ten different letters, i.e. they use all ten digits, and have only one solution. SEND + MORE = MONEY is not a very good alphametic because it contains only eight letters and omits the digits 3 and 4.

Two of his "best" alphametics which you might like to solve are:

RAIN
+SNOW
=====
SLEET

TEACUP
+SAUCER
=======
BISCUIT

Michael also calls super-elegant alphametics with words which are numerals, for example:

ONE
+ TWO
+FIVE
=====
EIGHT

TWO
+THREE
+SEVEN
======
TWELVE

By the way, one is not restricted to addition when compiling alphametics.

Five-Suit Bridge

Some years ago a suggestion was made to add another suit to the standard pack of cards. Like the others, the fifth suit would consist of the usual 13 cards and suggestions for its name included Crowns, Anchors and Eagles.

Selected contract bridge clubs tried out the new 65-card packs. They even drew up draft rules for the principles of bidding and play. In five-suit bridge each player would be dealt 16 cards with the spare 65th card being turned face-up on the table during play.

To determine probability-based strategies for the standard 52-card pack, the patterns of the possible numbers of cards in each suit has long been known. The total number of such patterns is 39 of which the four most frequent are:

4 4 3 2
5 3 3 2
5 4 3 1
5 4 2 2

That is, for example, the most commonly occurring split of cards in a 13 card bridge hand is four cards from each of two suits, three from a third and two from the fourth.

As a preliminary to forming strategies for the five-suit pack it was necessary to know all the possible patterns for the distribution of numbers of cards from each suit in a 16-card hand. A couple of possibilities are

6 4 3 3 0
13 3 0 0 0

That is, in the first example, the sixteen card hand includes six cards from one suit, four from another, three from each of two suits and none from the fifth.

The question is, how many possible ways are there for the distribution of cards from each suit in the 16-card bridge hand?

Russell Dear is a Mathematician living in Invercargill