Asking Directions

From Henry Dudeney:

Imagine a man going to the North Pole. The points of the compass are, as everyone knows:

dudeney - asking directions

He reaches the Pole and, having passed over it, must turn about to look North. East is now on his left-hand side, West on his right-hand side, and the points of the compass therefore

dudeney - asking directions

… which is absurd. What is the explanation?

Click for Answer

Better Late …

Shizo Kanakuri disappeared while running the marathon in the 1912 Summer Olympics in Stockholm. He was listed as a missing person in Sweden for 50 years — until a journalist found him living quietly in southern Japan.

Overcome with heat during the race, he had stopped at a garden party to drink orange juice, stayed for an hour, then took a train to a hotel and sailed home the next day, too ashamed to tell anyone he was leaving.

There’s a happy ending: In 1966 Kanakuri accepted an invitation to return to Stockholm and complete his run. His final time was 54 years, 8 months, 6 days, 8 hours, 32 minutes and 20.3 seconds — surely a record that will last forever.

A Technicality

World War II ended in 1990.

When the Reich surrendered in 1945, there was no single German state for the Allies to negotiate with. So officially the war continued for 45 more years; the final treaty was signed when Germany reunified.

See also Burying the Hatchet.

Round Numbers

In 1986 The Mathematical Intelligencer published this story about devising a mnemonic for a famous constant:

For a time I stood pondering on circle sizes. The large computer mainframe quietly processed all of its assembly code. Inside my entire hope lay for figuring out an elusive expansion. Value: pi. Decimals expected soon. I nervously entered a format procedure. The mainframe processed the request. Error. I, again entering it, carefully retyped. This iteration gave zero error printouts in all–success. Intently I waited. Soon, roused by thoughts within me, appeared narrative mnemonics relating digits to verbiage! The idea appeared to exist but only in abbreviated fashion–little phrases typically. Pressing on I then resolved, deciding firmly about a sum of decimals to use–likely around four hundred, presuming the computer code soon halted! Pondering these ideas, words appealed to me. But a problem of zeros did exist. Pondering more, solution subsequently appeared. Zero suggests a punctuation element. Very novel! My thoughts were culminated. No periods, I concluded. All residual marks of punctuation = zeros. First digit expansion answer then came before me. On examining some problems unhappily arose. That imbecilic bug! The printout I possessed showed four nine as foremost decimals. Manifestly troubling. Totally every number looked wrong. Repairing the bug took much effort. A pi mnemonic with letters truly seemed good. Counting of all the letters probably should suffice. Reaching for a record would be helpful. Consequently, I continued, expecting a good final answer from computer. First number slowly displayed on the flat screen–3. Good. Trailing digits apparently were right also. Now my memory scheme must probably be implementable. The technique was chosen, elegant in scheme: by self reference a tale mnemonically helpful was ensured. An able title suddenly existed–“Circle Digits”. Taking pen I began. Words emanated uneasily. I desired more synonyms. Speedily I found my (alongside me) Thesaurus. Rogets is probably an essential in doing this, instantly I decided. I wrote and erased more. The Rogets clearly assisted immensely. My story proceeded (how lovely!) faultlessly. The end, above all, would soon joyfully overtake. So, this memory helper story is incontestably complete. Soon I will locate publisher. There a narrative will I trust immediately appear, producing fame. THE END.

The text explains itself: Count the letters in each word (a punctuation mark other than a period counts as a 0, and a digit stands for itself), and you’ll get the first 402 digits of π.

“Proof That a Man Can Be His Own Grandfather”

From The World of Wonders, 1883:

“There was a widow [Anne] and her daughter [Jane], and a man [George] and his son [Henry]. The widow married the son, and the daughter married the father. The widow was therefore mother [in law] to her husband’s father, and grandmother to her own husband. By this husband she had a son [David], to whom she was also great-grandmother. Now, the son of a great-grandmother must be grandfather or grand-uncle to the person to whom his mother was great-grandmother; but Anne was great-grandmother to him [David]. Therefore David is his own grandfather.”

Hood’s Magazine (1846) adds, “This was the case with a boy at a school at Norwich.”


Composed in 390 B.C., Aristophanes’ play Ecclesiazusae concludes with the name of a dish on which the characters plan to feast.

The word is lopadotemachoselachogaleokranioleipsanodrimupotrimmatosilphioliparomelitoaktakexhumeno-kichlepikossuphophattoperisteralektruonoptopiphallidokinklopeleioplagoosiraiobaphetragalopterugon. At 169 letters, it’s still the longest word in the Greek language.

Lord Combermere’s Ghost

combermere ghost

In 1891, Sybell Corbet took this photograph in the library of Combermere Abbey in Cheshire. The abbey’s owner, Lord Combermere, had just died after a London accident and was being buried that day in the family vault a few miles away.

Members of the family felt the figure in the chair was very like the dead man. But physicist William Barrett, noting that it was distinct only from the waist up, suggested that perhaps a manservant had sat down briefly during the 15 minutes that Corbet had left the shutter open.

Barrett had just published an article with these particulars in the Westminster Gazette when he received a letter from a Combermere relative. She shared his doubts, she said, but wanted to correct one error in the article. “You say he had not lost his legs,” she wrote, “but he died from an accident in which they were so much injured, he could never have used them again. He was run over by a wagon at Knightsbridge, crossing the street, and only lived a few weeks.”