I show you three cards. One is white on both sides, one is black on both sides, and one is white on one side and black on the other. I shake them in a hat, remove one at random, and place it on a table. The side that’s face up is black. What’s the probability that the other side is also black?
Hint: It’s not 1/2.
In 1626 Peter Minuit, first governor of New Netherland, purchased Manhattan Island from the Indians for about $24. … Assume for simplicity a uniform rate of 7% from 1626 to the present, and suppose that the Indians had put their $24 at interest at that rate … and had added the interest to the principal yearly. What would be the amount now, after 280 years? 24 × (1.07)280 = more than 4,042,000,000. [The current value of Manhattan is] a little more than $4,898,400,000. … The Indians could have bought back most of the property now, with improvements; from which one might point the moral of saving money and putting it at interest!
— W.F. White, A Scrap-Book of Elementary Mathematics, 1908
Take any number and rearrange its digits to form another number.
Subtract one from the other. The difference will always be divisible by 9.
Schoolmaster: Suppose x is the number of sheep in the problem.
Pupil: But, sir, suppose x is not the number of sheep.
Mathematician J.E. Littlewood remarks: “I asked Prof. Wittgenstein was this not a profound philosophical joke, and he said it was.”
Lend me $10, but give me only half of it.
Then you’ll owe me $5, and I’ll owe you $5, and we’ll be even.
Nothing is heavier than lead.
Feathers are heavier than nothing.
Therefore feathers are heavier than lead.
“Ignorance more frequently begets confidence than does knowledge.” — Charles Darwin
Born in 1804, Zerah Colburn was thought to be mentally retarded until the age of 7, when his father overheard him solving multiplication problems for other children and discovered he was a prodigy. From the 1872 autobiography of Amos Kendall, with whom he boarded briefly:
He could multiply together any two numbers under a hundred in less than a minute. He could tell, apparently without thought, how many days there are in any number of years less than thirty, and in any number over thirty and up to a hundred upon a minute’s reflection. After being told the denominations of weights and measures, he would reduce one to another with the greatest readiness. He answered correctly the question, ‘How many gills are there in three barrels?’ The question, ‘How many are 25 × 25 + 35 × 35 +45 × 45?’ he answered correctly with little hesitation. He readily multiplied any number over a hundred by any number less. In less than a minute he answered correctly the question, ‘How many days are there in seventy-three years?’
“What rendered his performances more wonderful was, that he did not know a figure when written, and could not count more than fifty. How he knew the names of larger numbers was a mystery, and he was sometimes embarrassed in making his answers understood. After he had stated correctly the number of days in a given number of years, he was asked how many hours there were. He said he did not know the number of hours in a day. On being told it was twenty-four he immediately gave a correct answer.”
A man deposited $50 in a savings account, then withdrew it in various sums. When he’d recovered his $50 he was surprised to find $1 left in the account, though it had drawn no interest. When he inquired, the bank produced this ledger:
