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Mathematical Brain Benders: Second Miscellany of Puzzles

Stephen Barr
Dover Publications
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Underwood Dudley
, on

This is the title given by Dover in 1982 to its reprint of Barr’s 1969 2nd Miscellany of Puzzles, originally published by Macmillan.

There are 65 problems, followed by 50 “short puzzles, more or less from everyday life”. Almost all 115 have the advantage of being original, not to be found in other problem books, and the disadvantage of mostly being insoluble by ordinary readers.

You are not, repeat not, going to be able to place seven tiles on a scrabble board to get a score of 1148, even if I give you the hint that the word formed is “tranquilizingly”. At the other extreme, there is the problem of finding the number of positive two-digit integers, but, to keep readers from counting them on their fingers, there a time limit of thirty seconds. That problem was an exception: most problems I wouldn’t think of trying to solve, knowing that I would fail.

That is not to say that they are not entertaining because they are, their statements as well as their solutions. The author has wit as well as ingenuity. Geometry predominates. Knowing some, and some elementary algebra are the only mathematical prerequisites.

The other prerequisite is the ability to be struck by the lightening of insight at will. For example, problem 22 is the letter subtraction ROME ‒ SUM = RUSE. Proceeding as a normal person would, I rewrote it as RUSE + SUM = ROME and noted that M would have to be zero. But then S + U is 10, which implies that R + 1 = R, so that’s that: there is no solution. Well, yes there is: if R = D, O = C, M = X, E = I, S = L, and U = X then the Roman numeral subtraction is correct. Even with the indicators “Rome” and “ruse” I didn’t get that and I bet that you wouldn’t either. That doesn’t subtract from the pleasure of reading the solution.

Cleverness abounds. Problem 36 in the everyday life section asks how many kings were crowned in England since 1066. The answer is one. King James VI of Scotland became King James I of England in 1603. The other kings were all princes, dukes, or something like that before they were crowned.

This is a book well worth having.

Woody Dudley did rather well on the 1956 Putnam Examination (a two-digit finish) but his problem-solving abilities have gone a long way downhill since then.


  Owls' Eggs
  Conical Helix
  The Owl Island Flag
  Pseudo-Moebius Strip
  The Butler and the Crumbs
  The Three Clocks
  Slit Strips
  The Pot on the Crosspiece
  For Scrabble Players
  Area of Roof
  The Two Pyramids
  The Man Who Gave up Smoking
  Tetrahedron Angles
  Squares on a Circle
  Three Coins
  Two Coins
  The Coin Collector's Nightmare
  The Hi-Phi Set
  The Hauberk
  More Origametry
  Unique Parts of Letters
  For Phi Fans
  The Truck Gardens
  Phi Origametry
  The Cockeyed Kite
  More Phi Origametry
  The Bookmark
  Snow on the Roof
  Drafting Puzzle
  The Psychodelic Cube
  Construction Problem
  A Walk in a Field
  More Diagonals
  Short Proof (Cut Cube)
  Polyhedral Model
  Dihedral Angles
  Cheese Wedges
  The Poisoned Glass
  To Cover a Circle
  Pure Origami Solution
  The Flat Pan
  The Siamese Moebius Strip
  The Nine Digits
  Minimum Area
  Cocyclic Points
  The Tilted Carton
  Topology Puzzle
  The Vanadium Steel Clothesline
  The Balance
  Hydraulic Inference
  The Striped Whatsis
  The Terri Turnover
  The Heavy Chest
  The Pile and the Patriot
  The Pillar of Chios
  Literary Quiz
  Thunder on the Right
  Two Triangles