- FOUR contains four letters.
- TEN is spelled with ten raised dots in Braille.
- TWELVE is worth 12 points in Scrabble.
- FIFTEEN is spelled with 15 dots and dashes in International Morse Code.
TWENTY-NINE contains 29 straight lines — if you don’t count the hyphen.
At the 1939 World’s Fair, San Francisco Seals catcher Joe Sprinz tried to catch a baseball dropped from the Goodyear blimp 1,200 feet overhead.
Sprinz knew baseball but he hadn’t studied physics — he lost five teeth and spent three months in the hospital with a fractured jaw.
3685 = (36 + 8) × 5
What do these sentences have in common?
They’re all precisely the same length.
You’re overseeing a murder trial. The defendant will be hanged if his crime is judged to be both willful and premeditated. You poll the jurors:
A majority think it was willful, and a majority think it was premeditated, so you order the death penalty. As he’s dragged off to the gallows, the defendant screams that this is unfair and swears that his ghost will return for revenge.
You think nothing more of this until the evening, when a strange thought occurs to you. If you’d simply asked the jurors, “Should this man receive the death penalty?”, most would have voted no — only one of the three jurors believed that the crime was both willful and premeditated. Was your own reasoning unsound?
And who’s that behind you — ?
2502 = 2 + 502
Zhuangzi and Huizi were strolling along the dam of the Hao Waterfall when Zhuangzi said, ‘See how the minnows come out and dart around where they please! That’s what fish really enjoy!’
Huizi said, ‘You’re not a fish — how do you know what fish enjoy?’
Zhuangzi said, ‘You’re not I, so how do you know I don’t know what fish enjoy?’
Huizi said, ‘I’m not you, so I certainly don’t know what you know. On the other hand, you’re certainly not a fish — so that still proves you don’t know what fish enjoy!’
Zhuangzi said, ‘Let’s go back to your original question, please. You asked me how I know what fish enjoy — so you already knew I knew it when you asked the question. I know it by standing here beside the Hao.’
– Zhuangzi, China, fourth century B.C.
Arithmetic is easy in Spanish — just rearrange letters:
UNO + CATORCE = CUATRO + ONCE
DOS + TRECE = TRES + DOCE
DOCE + TRES = TRECE + DOS
Lewis Carroll offered this proof that all triangles are isosceles:
Let ABC be any triangle. Bisect BC at D, and from D draw DE at right angles to BC. Bisect the angle BAC.
(1) If the bisector does not meet DE, they are parallel. Therefore the bisector is at right angles to BC. Therefore AB = AC, i.e., ABC is isosceles.
(2) If the bisector meets DE, let them meet at F. Join FB, FC, and from F draw FG, FH, at right angles to AC, AB.
Then the triangles AFG, AFH are equal, because they have the side AF in common, and the angles FAG, AGF equal to the angles FAH, AHF. Therefore AH = AG, and FH = FG.
Again, the triangles BDF, CDF are equal, because BD = DC, DF is common, and the angles at D are equal. Therefore FB = FC.
Again, the triangles FHB, FGC are right-angled. Therefore the square on FB = the [sum of the] squares on FH, HB; and the square on FC = the [sum of the] squares on FG, GC. But FB = FC, and FH = FG. Therefore the square on HB = the square on GC. Therefore HB = GC. Also, AH has been proved equal to AG. Therefore AB = AC; i.e., ABC is isosceles.
Therefore the triangle ABC is always isosceles. Q.E.D.
2187 = (2 + 18)7
Mathematician Thomas Storer offers a foolproof way to foretell the future: Flip a penny and ask it a yes-or-no question. Heads means yes, tails means no.
How can you be sure the answer is accurate? Simple: Flip it again and ask, “Will your present answer have the same truth value as your previous answer?”
- Suppose the answer is yes. This is either true or false. If it’s true, then the original response was true. If it’s false, then the truth value of the original response is not false, i.e., it’s true.
- If the answer to the second question is no, this too is either true or false. If it’s true, then the original response was true. If it’s false, then the original response was not false, i.e., true.
Since all the outcomes agree, the penny’s original response is guaranteed to be correct.
Raymond Smullyan doesn’t believe in astrology.
When asked why, he says, “I’m a Gemini.”
Light travels 186,000 miles per second. The average diameter of Earth’s orbit is 186 million miles.
So, on average, sunlight reaches us in a neat 500 seconds.
“Yields a falsehood when preceded by its quotation” yields a falsehood when preceded by its quotation.
Now I will a rhyme construct,
By chosen words the young instruct.
Cunningly devised endeavour,
Con it and remember ever.
Widths in circle here you see,
Sketched out in strange obscurity.
Count the letters in each word.
The Professor brightened up again. ‘The Emperor started the thing,’ he said. ‘He wanted to make everybody in Outland twice as rich as he was before — just to make the new Government popular. Only there wasn’t nearly enough money in the Treasury to do it. So I suggested that he might do it by doubling the value of every coin and bank-note in Outland. It’s the simplest thing possible. I wonder nobody ever thought of it before! And you never saw such universal joy. The shops are full from morning to night. Everybody’s buying everything!’
– Lewis Carroll, Sylvie and Bruno
Your vote will make a difference only if it breaks a tie or creates one.
This is very unlikely to be the case.
So why vote?
99 + 19 + 29 + 99 + 89 + 59 + 19 + 59 + 39 = 912985153
When University College physicist Denis Osborne visited Mkwawa Secondary School in Iringa, Tanzania, in 1963, he little expected the question he got from student Erasto Mpemba:
“If you take two similar containers with equal volumes of water, one at 35°C and the other at 100°C, and put them into a freezer, the one that started at 100°C freezes first. Why?”
The other students derided Mpemba, but he was right — in cooking class he’d noticed that hot ice cream mixes froze more quickly than cold ones.
Osborne confirmed the effect and shared a publication with Mpemba in 1969. What’s behind “the Mpemba effect” is still something of a mystery — it seems to be a combined result of supercooling, convection, evaporation, and the insulating effect of frost. (If you want to conduct your own experiment, start with containers at 35°C and 5°C.)
Clearly S is positive. Now multiply each side by 2:
But that’s just the same as S minus 1.
And if 2S = S – 1, then S = -1.
So -1 is positive.
You can multiply these two numbers by simply jumbling their digits:
Remarkably, the same thing happens when you square their product: