Take a whole number, reverse the order of its digits, and subtract one from the other. The difference will always be evenly divisible by 9.
Does this remain true if we just scramble the digits of the first number, rather than reversing them?
Round and Round
‘I had quite a bit of fun playing hide-and-seek with a squirrel,’ he said. ‘You know that little round glade with a lone birch in the centre? It was on this tree that a squirrel was hiding from me. As I emerged from a thicket, I saw its snout and two bright little eyes peeping from behind the trunk. I wanted to see the little animal, so I started circling round along the edge of the glade, mindful of keeping the distance in order not to scare it. I did four rounds, but the little cheat kept backing away from me, eyeing me suspiciously from behind the tree. Try as I did, I just could not see its back.’
‘But you have just said yourself that you circled round the tree four times,’ one of the listeners interjected.
‘Round the tree, yes, but not round the squirrel.’
‘But the squirrel was on the tree, wasn’t it?’
‘So it was.’
‘Well, that means you circled round the squirrel too.’
‘Call that circling round the squirrel when I didn’t see its back?’
‘What has its back to do with the whole thing? The squirrel was on the tree in the centre of the glade and you circled round the tree. In other words, you circled round the squirrel.’
‘Oh no, I didn’t. Let us assume that I’m circling round you and you keep turning, showing me just your face. Call that circling round you?’
‘Of course, what else can you call it?’
‘You mean I’m circling round you though I’m never behind you and never see your back?’
‘Forget the back! You’re circling round me and that’s what counts. What has the back to do with it?’
— Yakov Perelman, Mathematics Can Be Fun, 1927
The High Life
From the Strand, July 1903:
The curious photograph which is here reproduced shows the well-known inventor of flying-machines, M. Santos Dumont, perched upon what looks like an abnormally lofty office-stool, accompanied by a friend in a similar position. The reason for this peculiarity lies in the fact that M. Santos Dumont is so accustomed to the sensation of being elevated above the earth that he feels more at home when he is so, even at meal-times.
This sounds like a joke, but the New York Herald tells of a dinner Santos-Dumont held in Paris that year:
From tables seven feet from floor to cloth the viands and wines were served, while the waiters attending to their wants walked about on stilts. The chairs, with their long, thin legs, were reached by mounting a short flight of portable steps.
Industrialist C.K.G. Billings had held a dinner on horseback that March in New York; possibly Santos-Dumont had taken that as inspiration. Here are a few more photos.
Stellate Thaumaturgy
Exemplary
In a dream someone said to me, ‘Any general thesis which is put forward without a concrete example is therein badly presented’. That was all he said, and I was about to point out the irony that in merely putting forward this thesis by means of a general statement the speaker had failed his own requirement of providing an example when it suddenly occurred to me, as I exclaimed to him, ‘Ah, I see. Your putting forward this thesis without an example is itself the concrete example’. But when I awoke I realized there was a problem here. If indeed the speaker is credited with having given me a concrete example of an example-less bad presentation, then that credit must be immediately withdrawn, because what he has given me is not an example of an example-less bad presentation. But if it is not an example, then it must once again be received as an example of example-less presentation, but then it once again is not an example, and so on forever.
— Arnold Zuboff, in Analysis, July 1992
Oh
A garrulous barber asked the Macedonian king Archelaus, “How shall I cut your hair?”
He answered, “In silence.”
(From Plutarch.)
Variant
A “Home Counties version” of the Lord’s Prayer:
Our Farnham which art in Hendon, Harrow be thy Name. Thy Kingston come. Thy Wimbledon in Erith, as it is in Heston. Give us this day our Leatherhead. And forgive us our Westminsters, as we forgive them that Westminster against us. And lead us not into Thames Ditton, but deliver us from Ealing. For thine is the Kingston, the Purley, and the Crawley, for Iver and Iver. Crouch End.
I don’t think anyone knows who wrote it. See The Author’s Tale.
Second Thoughts
On the Bench his lips would often be seen to move, but no sound proceeding from them would be heard by the Bar. The associate sitting beneath him could tell another tale. … ‘What a damned fool that man is!’ — then, after an interval, ‘Eh, not such a damned fool as I thought;’ then another interval. ‘Egad, it is I that was the damned fool.’
— J.B. Atlay on Lord Lyndhurst, in The Victorian Chancellors, 1906
Topsy Turvy
An acrostic by Robert Blackwell, 1868:
Turn this book and at us look,
Heed our features, too,
Expressive, fine, our faces shine,
To please such folks as you;
With heads but four, we want no more,
Our eyes give us no light;
Our ears are deaf, but yet no grief
Disturbs us day nor night;
Deprived of feet we can not walk
In houses where we go,
The reason why we do not sigh,
Is left for you to know.
Ever free from care are we,
So turn this book, and at us look.
Reading the first letter in each line produces the phrase “The Two Oddities.” Inverting the book gives the answer to the riddle: The “four heads” are actually one carefully devised figure — each face is the other upside down:
The 21-Card Trick
A performer takes 21 cards from a standard deck and shuffles them. A player notes one at random. The performer deals out the cards into three columns of seven cards each. The player indicates the column that contains her card. Twice more the performer deals out the cards into three columns and the player identifies the one containing her card. At this point the performer identifies the card.
How is this done? The trick works automatically so long as, in taking up the cards, the performer always puts the chosen pile between the other two. After the first deal, the chosen card will fall in one of positions 8-14; after the second deal, it will reach position 10-12; and after the last deal, it will be the 11th card in the assembled packet (at which point the performer can reveal it however he pleases).
This illustration, by CMG Lee, demonstrates the same principle using 27 cards. At each step, the pile containing the chosen card is shaded yellow; the numbers correspond to the step numbers. In this case the chosen card always finds its way to the 14th position.
Here’s an animation with 21 cards, in which the chosen card, marked with an X, finds its way to the 11th position:
