Outside the Box

Tim Krabbé published an eye-opening problem in Schaakbulletin in 1972. White must mate in 2 from this position:

vertical castling

He does so with 1. e8=R! Kg2 2. O-O-O-O-O-O#:

vertical castling

O-O-O-O-O-O denotes “vertical castling” — the king castles with the new rook on e8. Amazingly, this was arguably legal at the time — here’s how the rules defined castling:

“The king is transferred from its original square, two squares toward the rook; then that rook toward which the king has moved is transferred over the king to the square immediately adjacent to the king.”

All other stipulations are met: Neither the king nor the rook has moved previously, and the king passes through no square guarded by Black.

So, legal, right? Alas, after much debate in Dutch and Belgian chess columns, FIDE revised its rules to refer to a rook “on the same rank.” Some people have no imagination.

01/30/2012 UPDATE: I find the same idea mentioned in the April 1970 issue of the Journal of Recreational Mathematics — David Silverman says he proposed an “impossible” two-move checkmate, “a problem that generated a lot of heat,” for the Litton Problematical Recreations series following Richard Epstein’s discovery of a similar loophole in Hoyle’s Book of Rules. This anticipates Krabbé’s publication by two years.

| Entertainment

“A Fiery Wind”

Out in Cheatham county about noon on Wednesday — a remarkably hot day — on the farm of Ed. Sharp, five miles from Ashland, a sort of whirlwind came along over the neighbouring woods, taking up small branches and leaves of trees and burning them in a sort of flaming cylinder that travelled at the rate of about five miles an hour, developing size as it travelled. It passed directly over the spot where a team of horses were feeding and singed their manes and tails up to the roots; it then swept towards the house, taking a stack of hay in its course. It seemed to increase in heat as it went, and by the time it reached the house it immediately fired the shingles from end to end of the building, so that in ten minutes the whole dwelling was wrapped in flames. The tall column of travelling caloric then continued its course over a wheat field that had been recently cradled, setting fire to all the stacks that happened to be in its course. Passing from the field, its path lay over a stretch of woods which reached the river. The green leaves on the trees were crisped to a cinder for a breadth of 20 yards, in a straight line to the Cumberland. When the ‘pillar of fire’ reached the water, it suddenly changed its route down the river, raising a column of steam which went up to the clouds for about half-a-mile, when it finally died out. Not less than 200 people witnessed this strangest of strange phenomena, and all of them tell substantially the same story about it. The farmer, Sharp, was left houseless by the devouring element, and his two horses were so affected that no good is expected to be got out of them in future. Several withered trees in the woods through which it passed were set on fire, and continue burning still.

– Nashville, Tenn., Press, quoted in Symons’s Monthly Meteorological Magazine, September 1869

| Oddities

Red Menace

http://www.google.com/patents/about?id=WltCAAAAEBAJ

Ladies! Do you look like the loser of a tomato-eating contest? Do children mistake you for Bozo the Clown? Perhaps you’re incapable of applying lipstick properly!

Let’s face it, the task is practically impossible. That clumsy tube, those bewildering lips — where do you start? How do you finish? It’s a wonder you haven’t been injured or killed.

Marie Helehan’s lipstick stencil, patented in 1937, offers “a clean-cut accurate and symmetrical outline” in which to work. Now we just need a mascara gun …

| Society · Technology

Nature, Nurture

Identical twins Jack Yufe and Oskar Stohr were born in 1932 to a Jewish father and a Catholic mother. Their parents divorced when the boys were six months old; Oskar was raised by his grandmother in Czechoslovakia, where he learned to love Hitler and hate Jews, and Jack was raised in Trinidad by his father, who taught him loyalty to the Jews and hatred of Hitler.

At 47 they were reunited by scientists at the University of Minnesota. Oskar was a conservative who enjoyed leisure, Jack a liberal workaholic. But both read magazines from back to front, both wore tight bathing suits, both wrapped rubber bands around their wrists, both liked sweet liqueur and spicy foods, both had difficulty with math, both flushed the toilet before and after using it — and both enjoyed sneezing suddenly in elevators to startle other passengers.

See Doppelgangers.

| Oddities · Science & Math

“Imitation”

Calm and implacable,
Eyeing disdainfully the world beneath,
Sat Humpty-Dumpty on his mural eminence
In solemn state:
And I relate his story
In verse unfettered by the bothering restrictions of rhyme or metre,
In verse (or “rhythm,” as I prefer to call it)
Which, consequently, is far from difficult to write.

He sat. And at his feet
The world passed on — the surging crowd
Of men and women, passionate, turgid, dense,
Keenly alert, lethargic, or obese.
(Those two lines scan!)

Among the rest
He noted Jones; Jones with his Roman nose,
His eyebrows — the left one streaked with a dash of gray –
And yellow boots.
Not that Jones
Has anything in particular to do with the story;
But a descriptive phrase
Like the above shows that the writer is
A Master of Realism.

Let us proceed. Suddenly from his seat
Did Humpty-Dumpty slip. Vainly he clutched
The impalpable air. Down and down,
Right to the foot of the wall,
Right on to the horribly hard pavement that ran beneath it,
Humpty-Dumpty, the unfortunate Humpty-Dumpty,
Fell.

And him, alas! no equine agency,
Him no power of regal battalions –
Resourceful, eager, strenuous –
Could ever restore to the lofty eminence
Which once was his.
Still he lies on the very identical
Spot where he fell — lies, as I said, on the ground,
Shamefully and conspicuously abased!

– Anthony C. Deane, in Carolyn Wells, A Parody Anthology, 1922

| Poems

A Natural Seat

http://en.wikipedia.org/wiki/File:Krubsack_chair.jpg

John Krubsack grew a chair. The Wisconsin banker planted 32 box elders in 1903, and as they grew he grafted them into a living piece of furniture.

In 1911 he began lending “The Chair That Grew” to international exhibitions; today it’s on display at his nephew’s furniture store.

| Oddities

Hendecadivisibility

To discover whether a number is divisible by 11, add the digits that appear in odd positions (first, third, and so on), and separately add the digits in even positions. If the difference between these two sums is evenly divisible by 11, then so is the original number. Otherwise it’s not.

For example:

11 × 198249381729 = 2180743199019

Sum of digits in odd positions = 2 + 8 + 7 + 3 + 9 + 0 + 9 = 38

Sum of digits in even positions = 1 + 0 + 4 + 1 + 9 + 1 = 16

38 – 16 = 22

22 is a multiple of 11, so 2180743199019 is as well.

| Science & Math