Take any number and rearrange its digits to form another number.
Subtract one from the other. The difference will always be divisible by 9.
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:
2 + 5 + 6 = 13; 132 = 169
1 + 6 + 9 = 16; 162 = 256
83 = 512; 5 + 1 + 2 = 8
273 = 19683; 1 + 9 + 6 + 8 + 3 = 27