A pleasant anecdote is told of Partridge, the celebrated almanac maker. In traveling on horseback into the country he stopped for his dinner at an inn, and afterward called for his horse that he might reach the next town, where he intended to sleep. ‘If you would take my advice, sir,’ said the ostler, as he was about to mount his horse, ‘you will stay where you are for the night, as you will surely be overtaken by a pelting rain.’ ‘Nonsense, nonsense,’ said the almanac maker, ‘there is sixpence for you, my honest fellow, and good afternoon to you.’ He proceeded on his journey, and sure enough he was well drenched in a heavy shower. Partridge was struck with the man’s prediction, and being always intent on the interest of his almanac, he rode back on the instant, and was received by the ostler with a broad grin. ‘Well, sir, you see I was right after all.’ ‘Yes, my lad, you have been so, and here is a crown for you, but I give it you on condition that you tell me how you knew of this rain.’ ‘To be sure, sir,’ replied the man; ‘why the truth is we have an almanac in our house called Partridge’s Almanac, and the fellow is such a notorious liar, that whenever he promises us a fine day we always know that it will be the direct contrary.’

— The Golden Rule, and Odd-Fellows’ Family Companion, Oct. 16, 1847

Here is a curious old story that is something like a puzzle: A crocodile stole a baby, ‘in the days when animals could talk,’ and was about to make a dinner of it. The poor mother begged piteously for her child. ‘Tell me one truth,’ said the crocodile, ‘and you shall have your baby again.’ The mother thought it over, and at last said: ‘You will not give it back.’ ‘Is that the truth you mean to tell?’ asked the crocodile. ‘Yes,’ replied the mother. ‘Then by our agreement I keep him,’ added the crocodile; ‘for if you told the truth I am not going to give him back, and if it is a falsehood, then I have also won.’ Said she: ‘No, you are wrong. If I told the truth you are bound by your promise; and, if a falsehood, it is not a falsehood, until after you have given me my child.’ Now, the question is, who won?

— Pennsylvania School Journal, March 1887

The first few powers of 5 share a curious property — their digits can be rearranged to express their value:

25 = 5²
125 = 5^{1 + 2}
625 = 5^{6 – 2}
3125 = (3 + (1 × 2))⁵
15625 = 5⁶ × 1²⁵
78125 = 5⁷ × 1⁸²

It’s conjectured that all powers of 5 have this property. But no one’s proved it yet.

Suppose you borrowed $10 from Tom and $10 from Bob. On your way to repaying them you are robbed of everything but the $10 you had hidden in your shirt pocket. By no fault of your own, you now face the following paradoxical dilemma:

(1) You are obligated to repay Tom and Bob.
(2) If you pay Tom you cannot repay Bob.
(3) If you repay Bob you cannot repay Tom.
(4) You cannot honor all your obligations: in the circumstances this is impossible for you. (By (1)-(3).)
(5) You are (morally) required to honor all your obligations.
(6) You are not (morally) required to do something you cannot possibly do (ultra posse nemo obligatur).

— Nicholas Rescher, Paradoxes, 2001

String together the numbers 1 through 19 in reverse order:

19181716151413121110987654321

Fittingly, the resulting number is evenly divisible by 19.

6205 = 38² + 69²
3869 = 62² + 05²

5965 = 77² + 06²
7706 = 59² + 65²

Suppose that in one night all the dimensions of the universe became a thousand times larger. The world will remain similar to itself, if we give the word similitude the meaning it has in the third book of Euclid. Only, what was formerly a meter long will now measure a kilometer, and what was a millimeter long will become a meter. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I wake in the morning what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all. The most exact measures will be incapable of revealing anything of this tremendous change, since the yard-measures I shall use will have varied in exactly the same proportions as the objects I shall attempt to measure.

— Henri Poincaré, Science and Method, 1908

If we take a cube and label one side top, another bottom, a third front, and a fourth back, there remains no form of words by which we can describe to another person which of the remaining sides is right and which left. We can only point and say here is right and there is left, just as we should say this is red and that blue.

— William James, The Principles of Psychology, 1890