When in Rome

What number comes next in this series?

0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1

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The next number is 9. The numbers correspond to the Roman numerals hidden in English number names:

April 17, 2010January 24, 2013 | Puzzles

Road Work

I set out to run a 26.5-mile marathon hoping to average less than 9 minutes per mile. As I run, my friends measure my time along various mile-long segments of the course. On each mile that they measure — indeed, on each mile that it’s possible to measure, starting anywhere along the course — my time is exactly 9 minutes. Yet my average for the whole marathon is less than 9 minutes per mile.

How is this possible?

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Solution to Road Work: I run the first half-mile in 4 minutes and the next in 5 minutes, and continue alternating like this throughout the marathon. In this way I’ll cover any measured mile in 9 minutes. But because the “fast” segments outnumber the “slow” ones, my average pace for the whole run is less than 9 minutes per mile. This works because the course does not cover an even number of miles. From Frank Morgan, The Math Chat Book, 2000.

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April 15, 2010January 23, 2013 | Puzzles

Menagerie

How many pets do I have if all of them are dogs except two, all are cats except two, and all are fish except two?

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There are two possible answers here, thanks to the slipperiness of the word all: 1. I have a dog, a cat, and a fish. 2. I have two Denebian Slime Devils, or two Eight-Thumbed Mongolian Rat-Weasels, or two of anything-that’s-not-a-cat-dog-or-fish. I actually prefer the second answer. (Thanks, Remy.)

April 13, 2010January 23, 2013 | Puzzles

“Four Puzzles in One”

By Sam Loyd. Place the black king (a) where it can be checkmated on the move, (b) where it’s in stalemate, (c) where it’s in checkmate, and (d) where the three white pieces can’t be arranged to checkmate it.

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(a) a8, (b) h1, (c) e3, (d) g7.

April 10, 2010January 23, 2013 | Puzzles

Mate in Two

By G.A.A. Walker. White to play and checkmate all six black kings simultaneously with his second move.

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1. Bb3+ d5 (forced) 2. cxd6 e.p.######: From D. Littlewick, “Curiosities on the Chess-Board,” Strand, January 1910.

April 2, 2010January 23, 2013 | Puzzles

A Mysterious Windfall

A riddle by Isaac Newton:

Four people sat down at a table to play;
They play’d all that night, and some part of next day;
This one thing observ’d, that when all were seated,
Nobody play’d with them, and nobody betted;
Yet, when they got up, each was winner a guinea;
Who tells me this riddle I’m sure is no ninny.

Who are the players?

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Musicians.

March 30, 2010January 23, 2013 | Puzzles

Erin Go

Count these leprechauns:

vanishing leprechaun 1

Now swap the two upper panels and count again:

vanishing leprechaun 2

Where has the extra one been hiding?

March 24, 2010September 1, 2010 | Puzzles

Hidden in Sight

This puzzling verse, from a contributor named “Maude,” appeared in the Weekly Wisconsin of Sept. 29, 1888:

Perhaps the solvers are inclined to hiss,
Curling their nose up at a con like this.
Like some much abler posers I would try
A rare, uncommon puzzle to supply.
A curious acrostic here you see
Rough hewn and inartistic tho’ it be;
Still it is well to have it understood,
I could not make it plainer, if I would.

(In the second line, “con” means “contribution.”)

What are the concealed words?

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The first two letters of each line spell out PECULIAR ACROSTIC.

March 21, 2010January 23, 2013 | Puzzles

Cornered

One of Eduard Gufeld’s first chess coaches, A.A. Olshansky, offered him this problem:

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“White to mate in half a move.”

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“Lift the white knight just a little off the board.”

March 16, 2010January 23, 2013 | Puzzles

A Curious Exchange

Census Taker: How old are your three daughters?

Mrs. Smith: The product of their ages is 36, and the sum of their ages is the address on our door here.

Census Taker: (after some figuring) I’m afraid I can’t determine their ages from that …

Mrs. Smith: My eldest daughter has red hair.

Census Taker: Oh, thanks, now I know.

How old are the three girls?

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There must be at least two sets of three numbers whose product is 36 but that have the same sum. Trial and error shows these are (1, 6, 6) and (2, 2, 9), both of which add to 13. Mrs. Smith’s second statement is a “red hairing” — the eldest daughter’s hair color is unimportant, but the fact that Mrs. Smith has an eldest daughter implies that (1, 6, 6) can’t be the right answer. Thus her daughter’s ages are 2, 2, and 9. From Frank Morgan, The Math Chat Book, 2000. Some readers object that even twins are not precisely the same age, so the (1, 6, 6) group does contain an “eldest” daughter and can’t be ruled out on that basis. I think that’s a valid criticism.

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March 9, 2010January 23, 2013 | Puzzles