You’re in a pitch-black room with a clock that chimes the hour and also chimes once at each quarter hour. If you hear the clock chime once, what’s the longest you’ll have to wait to be sure what time it is?
Puzzles
A Topology Puzzle
Prayer Vigil
A puzzle by F. Nazarov from the May-June 1996 issue of Quantum:
On a certain familiar island, some residents always lie, and the others always tell the truth. The total population is 100. Each resident worships one of three gods, the sun god, the moon god, or the Earth god. One day a visitor asks each resident three questions:
- Do you worship the sun god?
- Do you worship the moon god?
- Do you worship the Earth god?
Sixty residents answer yes to the first question, 40 to the second, and 30 to the third. How many residents are liars?
Forefather
A problem from the Third Penguin Problems Book, 1946:
“Flutterby’s grandfather died in 1872. Flutterby died one hundred and thirty-one years after his grandfather was born. Their ages add up to one hundred and five years. When was Flutterby born?”
Chestnut
A Union Cipher
This baffling message illustrates a cipher adopted by the Union Army in 1862:
TO GEORGE C. MAYNARD, Washington
Regulars ordered of my to public out suspending received 1862 spoiled thirty I dispatch command of continue of best otherwise worst Arabia my command discharge duty of my last for Lincoln September period your from sense shall duties the until Seward ability to the I a removal evening Adam herald tribune.
PHILIP BRUNER
The address and signature are “covers” that don’t enter into the cipher. The first word, Regulars, is a code indicating that the original message had been written in five columns of nine words each. Tribune, herald, spoiled, Seward, for, and worst are null words; Lincoln is code for Louisville, Kentucky; Adam means General Henry Wager Halleck; and Arabia is code for Major General Don Carlos Buell. The word Period indicates a full stop. This had been the original message:
Louisville, Kentucky September thirty 1862 General Halleck: (Adam) (period) I received last evening your dispatch suspending my removal from command. Out of a sense of public duty, I shall continue to discharge the duties of my command to the best of my ability until otherwise ordered. D.C. Buell, Major General
This message had been enciphered by reading up the fourth column, down the third, up the fifth, down the second, and up the first; inserting the null words; and encoding the most sensitive particulars. The system worked well until July 1864, when Union cipher operator Stephen L. Robinson was captured by Confederate guerrillas and the key seized.
(John Laffin, Codes and Ciphers Secret Writing Through the Ages, 1964.)
Conclusions
From John Boyce Bennett’s 1980 logic textbook Rational Thinking:
If it’s false that no dopips are fraks, characterize each of these propositions as true, false, or doubtful:
a. All dopips are fraks.
b. Few dopips are fraks.
c. Some dopips are fraks.
d. No fraks are dopips.
e. Some dopips are not fraks.
Black and White
Census Trouble
A curious puzzle by Stanley Rabinowitz, from the Spring 1984 issue of Pi Mu Epsilon Journal:
In the little hamlet of Abacinia, two different base systems are used, and everyone speaks the truth. One resident said, “26 people use my base, base 10, and only 22 people speak base 14.” Another said, “Of the 25 residents, 13 are bilingual and 1 is illiterate.” How many people live in Abacinia?
Track Record
A problem from the October 1964 issue of Eureka, the journal of the Cambridge University Mathematical Society:
“At noon precisely, a train leaves A for B, and another leaves B for A. They pass after 51 minutes. Each train stays 27 minutes at its destination and then returns by the same route. The trains from A and B travel throughout with constant speeds of 23 m.p.h. and 39 m.p.h., respectively. At what time do they pass for the second time?”
