Problems for Metagrobologists
by David Singmaster
As a verb, the English word puzzle has two conflicting meanings: 1) to surprise, confuse; 2) to solve, resolve one's confusion. David Singmaster - the author of the new puzzles book - may have had that in mind by naming his book "Problems for Metagrobologists". While he began referring to himself as a metagrobologist years ago, outside the limited circle of professional puzzlists, the term is not well known. So the title is both surprising and inviting to puzzle out what might the book be about. David helps the reader in the first paragraphs of Introduction:
In case you don't already know, the Oxford English Dictionary's (OED) entry for METAGROBOLIZE describes it as humorous. Rabelais used metagraboulizer and Cotgrave (1611) translates it as "to dunce upon, to puzzle, or (too much) beate the braines about." The OED gives: To puzzle, mystify To puzzle out.
As an expert puzzle historian, David continues with two more paragraphs and additional references - these you'll have to consult for yourself. I am puzzled by that word that has no known etymology. Taking a clue from the OED's entry, I am puzzling. "Meta-" and "logos" are of Greek origins, meaning, "after, beyond, over" and "discourse, study", respectively. The "grob" part may be a distortion from Rabelais' "grab" that in English could suggest "grabbing attention" so that "metagrobolize" could mean a "study of super attention grabbers". Similarly, if "grob" is a distortion of "grope", "metagrobologist" could be a designation for somebody lost deeply in thought, perhaps in an attempt to puzzle out a problem. For a Russian speaker, the word "metagrobology" is especially suggestive, for "grob" in Russian stands for coffin. "Metagrobology" then comes out as the study of what comes after one finds himself in a coffin or the highway of getting there, perhaps via too much puzzling.
David Singmaster's book is a collection of puzzles, many original, many variations on older ones. One trait sets the present book apart from other puzzle collections. David is a well known historian of recreational mathematics and the most trusted address for puzzle sources. He freely shares his knowledge with his readers. Other authors of puzzle collections commonly present answers and sometimes solutions to their problems, seldom their history or references. For example, H. E. Dudeney (1857-1930) authored a puzzle of building a house on a piece of land in the shape of an equilateral triangle. The puzzle asked for the shortest total sum of the distances from the house to the bounding roads, without so much as mentioning Vincenzo Viviani (1622-1703) whose well known theorem provides the contents for the puzzle.
A good example of David's approach is, for example, the puzzle of ferrying couples across the river. The puzzle is attributed to Alcuin of York (c800): three jealous husbands with their wives need to cross a river using a boat that only holds two people. No husband can stand his wife left with another male without him being present. The solution consists of 11 boat trips. We learn that in 1556 Tartaglia claimed a solution for four couples but at one point there were 3 wives and 2 husbands on a shore, with one wife taking the boat back which constitutes a break in the rules. In 1879 M. Cadet De Fonthenay suggested having an island in the river that could be used as a transition point. He found a 26 boat trips solution (without direct bank-to-bank trips across the river.) In 1917, Henry Dudeney found a solution in 17 crossings with a few direct crossings. In the solutions section, David proves that 26 is minimal under the imposed conditions, and shows a 16 trips improvement by one of his students on Dudeney's solution.
David combined the puzzles into 15 loosely thematic sections (this too is seldom done in puzzle books.) This helps the reader focus on the puzzles of his/her preference. Not every metagrobologist, especially, the amateurs among them, likes or has an inclination for solving any puzzle he or she comes across. I, for one, is less than enamoured with counting, say, triangles formed by a number of lines and line segments. But, with more than 200 (actually 221) puzzles, David Singmaster's book is in a position to satisfy readers of various tastes.
If I have a peeve concerning the book, this is David's occasional use (or the advice to use) computers to solve a puzzle. While programming may be construed as metagrobolizing in the sense of exercising one's brain, such exercise - in my view - goes on cross-purposes with solving the underlying puzzle. But, again, others (and David among them) find this activity as rewarding as puzzling the problem unaided by technology.
I believe the book will be welcome by amateur, as well as professional, metagrobologists. Many of the puzzles could be used as warm-up exercises to engender creative atmosphere in a math class. I am sure that many a math teacher will agree with this assessment.
The site contains several pages that refer to the book:
- Bicubal Domino
- Getting Your Rightful Share Back
- Constrained Intermarriages
- Fibonacci Tilings
- How Fast Does One's Shadow Grow?
- Advancing a Millenium Problem
Problems for Metagrobologists: A Collection of Puzzles with Real Mathematical, Logical or Scientific Content, by David Singmaster. World Scientific Publishing Co, 2016. Softcover, 246 pp, $28. ISBN 978-9814663649.