Archive | Puzzles

Here’s a puzzle I came up with this morning (though I’m sure others had thought of it before). We know that the sum of integers from 1 to n — let’s call it S1(n) — is n × (n+1) / 2. We know that the sum of the squares of integers from 1 to n […]

What are the earliest five constitutions of independent countries? [UPDATE: Why limit ourselves to five? Let’s just go no further than 1799. Also, I forgot the most important part: they must be written. Every country has a constitution, but most old ones are unwritten!] A bit of definitions and clarifications to start us off: The […]

I thought I’d repeat a puzzle that I first posted five years ago. Put these in order by moving the fewest names: Washington, Wilson, Johnson, Johnson, McKinley, Davis, Jackson, Taft, Kennedy Moving a name to between two other names, before the first name, or after the last name all count as one move. Thus, exchanging […]

Find a ten-digit number with the following two properties (in base 10, of course): A. The number contains each digit (from 0 to 9) exactly once. B. For every N from 1 to 10, the first N digits of the number are divisible by N. Thus, for instance, 1234567890 doesn’t work; while 1 is divisible […]

My friend Haym Hirsh developed these puzzles for G4G9, the ninth Gathering for [Martin] Gardner, and kindly agreed to let me blog them: Martin Gardner’s relative Dr. Art Renaming traveled widely across the U.S. and the world. Art maintained a diary in which he described some of the puzzling circumstances he experienced over the course […]

The Green Bag 2d has just published my The Numbers of the Constitution, a puzzle that begins: To what do the following numbers refer in the United States Constitution? … 1/5: 1/3: 3/5: … 5: … 12: … Three numbers greater than 1000: … Check out the whole item. Thanks to Larry Arnold, Linus Richard […]

What is the smallest positive integer that, when written out in standard English, does not yield any Google searches? Do not use “and”s, and do not use the format in which hundreds are counted using numbers greater than ten (e.g., “forty two hundred eighty two” — that’s acceptable standard English, but I just want to […]

Legalese puzzle: What is the meaning of “p/n/g,” which is sometimes used in case captions in Pennsylvania and occasionally New York? I’m not asking about “PNG,” which sometimes stands for “p/n/g,” but more often for Papua New Guinea, the Professional Numismatists Guild, or other things. UPDATE: Bleh and D.J., in the comments, were the first […]

Leonhard correctly finishes a Sudoku puzzle, and tells you: “That’s cool! When I look only at the upper left-hand 3 x 3 square of the puzzle, view each of the three-digit rows as a three-digit number, and add them together, I get 1000.” Is he telling the truth? An alternative version, if you prefer: You […]

People who follow federal criminal law know that it occupies Title 18 of the U.S. Code. Copyright law buffs know that the Copyright Act occupies Title 17. Why are they next to each other?

A puzzle from Michael Lorton: Most words that end in -tion or -sion are nouns, but some are also verbs: consider mention, proposition, question, section, and station. What words that end in -tion or -sion are verbs but not nouns? UPDATE: “Stunning, overwhelming thread victory.”

(but not of most other things) — a fun puzzle from Glen Whitman (Agoraphilia).

Fill in the blank in the following list: 1. Vermont, Connecticut, New Hampshire 2. Pennsylvania, Delaware, New Jersey 3. Indiana, Ohio, Kentucky 4. Arkansas, Mississippi, Tennessee 5. Iowa, Missouri, Nebraska 6. California, Colorado, Arizona 7. Washington, ______________, Oregon