Mathematical Brain Benders: Second Miscellany of Puzzles

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.