Some famous recreational mathematicians

Lewis Carroll

Pillow problems

A frequently quoted source of puzzles is Carroll’s collection of 72 ‘Pillow Problems’. These problems are math problems that he made up and then solved while lying in bed, hoping that this would help take his mind off his nightmares and frequent insomnia.

Calendars

Lewis Carroll loved ‘playing around’ with dates. Among his many inventions, Carroll thought up a method to find out on which day of the week a certain date falls. His method was not based on any ‘previous knowledge’ and did not involve counting.

Logic

Carroll went much deeper in the study of logic. His ‘Game of Logic’ was originally invented by Carroll as a pure game, but later on, became a very useful way to come to conclusions from any number of given words, sentences or statements.

Doublets

Another word game Lewis Carroll invented is known as ‘Doublets’. Given an initial word, you have to evolve it into a given, ‘end’ word in the least possible number of steps. There is just one rule to follow. All you have to do at each step is to replace one of the letters of the word with a different letter to obtain a new legal English word. The following example will make this clear. In this example, we will try to get from the word FOUR to FIVE in eight steps.

• In each step only one letter is replaced
• No letters can be added or taken away (the number of letters in the word is constant)
• All words have to be legal English words
• The first and last words count when counting the number of steps

FOUR – FOUL – FOOL – FOOD – FOND – FIND – FINE – FIVE

Henry Ernst Dudeney and Sam Loyd

The next recreational mathematicians we are going to meet are: Henry Ernst Dudeney and Sam Loyd. Dudeney was the better mathematician while Loyd is considered a better puzzlist. The reason that we mention them together, is that they frequently exchanged puzzles, that is until Loyd published Dudeney’s puzzles under his own name…

Now for some puzzles…

Can you solve these two puzzles of Dudeney and Loyd?

Dudeney:

Buns were being sold at three prices: one for a penny, two for a penny, and three for a penny. Some children (there were as many boys as girls) were given seven pennies to spend on these buns, each child to receive exactly the same value in buns. Assuming that all buns remained whole, how many buns, and of what types, did each child receive? (from: 536 Puzzles and Curious Problems)

Loyd:

While enjoying a giddy ride at the carousel Sammy propounded a puzzle which reflects much credit to his mental abilities:   ‘One third of the number of kids riding ahead of me, added to three-quarter of those riding behind me gives the correct number of children on this Merry-Go-Round’ is the way he puts it; but it will puzzle you quite a little to tell just how many riders there were at this whirling circus? (from: Sam Loyd’s Cyclopedia of Puzzles)

Martin Gardner

Gardner popularized math like no-one before, expanding the borders of what was considered recreational math to other fields such as art, magic, computer science and skepticism. Gardner wrote his column for 25 consecutive years, alongside over one hundred books on recreational math, popular science, wordplay, literature, skepticism and magic. He became an expert and prolific writer in all of these fields.

Puzzle time

Martin Gardner wrote about magic squares, mechanical puzzles and codes. He also popularized John Conway’s Game of Life, the predecessor of modern computer games and simulations.
Like Carroll, Dudeney and Loyd, Gardner published many puzzles. Here is a ‘quicky’ you might want to try yourselves.

How many months have 30 days? (from ‘The Unexpected Hanging’)