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.)

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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.

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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?

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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?”

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Rebus

https://commons.wikimedia.org/wiki/File:Six_moral_sentences_beginning_with_the_letter_T_LCCN2001706201.jpg

Currier & Ives published this lithograph in 1875: “Six moral sentences beginning with the letter T.” I can’t find the answers! My guesses:

True honesty brings prosperity.

Trace[?] the footsteps of the wise.

Those do well who never lie.

Tears of repentency are like diamonds.

Train yourself to be temperate.

That which is well earned is most comforting[?].

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Ah

From John Scott’s The Puzzle King, 1899:

“A locomotive with a truck is travelling over a straight level line at the rate of 60 miles an hour. A man standing at the extreme rear of the truck casts a small stone into the air in a perpendicular direction. The stone travels upward at an average rate of 30 feet per second for 3 seconds; the height of the man’s hand from ground when the stone leaves is 15 feet. At what distance behind the train will the stone strike the ground in its descent?”

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Hidato

https://commons.wikimedia.org/wiki/File:Hidato-Puzzle.svg

This logic puzzle game was invented by Israeli mathematician Gyora Benedek. The task is simple: Write a number in each blank square so that, in the finished diagram, a continuous chain of consecutive numbers connects the lowest number, 1, to the highest, 40. The numbers can connect horizontally, vertically, or diagonally. For example, the number 8 must go in the square above 7 because 7, 8, and 9 must occupy adjacent squares. Can you complete the rest of the diagram?

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Intermission

You’ve dealt about half the cards for a bridge game when you’re momentarily called away. When you return, no one can remember where you left off dealing. Without counting cards, how can you finish the deal accurately, so that each player receives the cards she’d have got if you hadn’t been interrupted?

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