Suppose we fill Yankee Stadium with 50,000 people and ask them to spend the day shaking hands with one another.
Prove that, at the end of the day, at least two participants will have shaken hands with the same number of people.
In Ralph Roister Doister (1553), Ralph asks a scrivener to compose a love letter to Dame Christian Custance. But when Matthew Merrygreek reads it for her, Dame Custance is shocked to hear an insulting diatribe. This is certainly not what Ralph intended, but the scrivener confirms that he copied the letter accurately, and Merrygreek read it verbatim and in full. What’s going on here?
Sweet mistress, whereas I love you nothing at all–
Regarding your substance and richness chief of all–
For your personage, beauty, demeanour and wit,
I commend me unto you never a whit.–
Sorry to hear report of your good welfare,
For (as I hear say) such your conditions are,
That ye be worthy favour of no living man,
To be abhorred of every honest man,
To be taken for a woman inclined to vice,
Nothing at all to virtue giving her due price.–
Wherefore, concerning marriage, ye are thought
Such a fine paragon, as ne’er honest man bought.–
And now by these presents I do you advertise
That I am minded to marry you in no wise.–
For your goods and substance, I can be content
To take you as ye are. If ye mind to be my wife,
Ye shall be assured, for the time of my life,
I will keep you right well from good raiment and fare–
Ye shall not be kept but in sorrow and care–
Ye shall in no wise live at your own liberty.
Do and say what ye lust, ye shall never please me;
But when ye are merry, I will be all sad;
When ye are sorry, I will be very glad;
When ye seek your heart’s ease, I will be unkind;
At no time in me shall ye much gentleness find,
But all things contrary to your will and mind,
Shall be done–otherwise I will not be behind
To speak. And as for all them that would do you wrong,
I will so help and maintain, ye shall not live long–
Nor any foolish dolt shall cumber you but I.
I, whoe’er say nay, will stick by you till I die.
Thus, good mistress Custance, the Lord you save and keep;
From me, Roister Doister, whether I wake or sleep–
Who favoureth you no less, ye may be bold,
Than this letter purporteth, which ye have unfold.
What number comes next in this series?
0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1
I set out to run a 26.5-mile marathon hoping to average less than 9 minutes per mile. As I run, my friends measure my time along various mile-long segments of the course. On each mile that they measure — indeed, on each mile that it’s possible to measure, starting anywhere along the course — my time is exactly 9 minutes. Yet my average for the whole marathon is less than 9 minutes per mile.
How is this possible?
How many pets do I have if all of them are dogs except two, all are cats except two, and all are fish except two?
By Sam Loyd. Place the black king (a) where it can be checkmated on the move, (b) where it’s in stalemate, (c) where it’s in checkmate, and (d) where the three white pieces can’t be arranged to checkmate it.
By G.A.A. Walker. White to play and checkmate all six black kings simultaneously with his second move.
A riddle by Isaac Newton:
Four people sat down at a table to play;
They play’d all that night, and some part of next day;
This one thing observ’d, that when all were seated,
Nobody play’d with them, and nobody betted;
Yet, when they got up, each was winner a guinea;
Who tells me this riddle I’m sure is no ninny.
Who are the players?
Count these leprechauns:
Now swap the two upper panels and count again:
Where has the extra one been hiding?
This puzzling verse, from a contributor named “Maude,” appeared in the Weekly Wisconsin of Sept. 29, 1888:
Perhaps the solvers are inclined to hiss,
Curling their nose up at a con like this.
Like some much abler posers I would try
A rare, uncommon puzzle to supply.
A curious acrostic here you see
Rough hewn and inartistic tho’ it be;
Still it is well to have it understood,
I could not make it plainer, if I would.
(In the second line, “con” means “contribution.”)
What are the concealed words?
One of Eduard Gufeld’s first chess coaches, A.A. Olshansky, offered him this problem:
“White to mate in half a move.”
Census Taker: How old are your three daughters?
Mrs. Smith: The product of their ages is 36, and the sum of their ages is the address on our door here.
Census Taker: (after some figuring) I’m afraid I can’t determine their ages from that …
Mrs. Smith: My eldest daughter has red hair.
Census Taker: Oh, thanks, now I know.
How old are the three girls?
From Sam Loyd:
Here is a map of the newly discovered cities and waterways on our nearest neighbor planet, Mars. Start at the city marked T, at the south pole, and see if you can spell a complete English sentence by making a tour of all the cities, visiting each city only once, and returning to the starting point.
When this puzzle originally appeared in a magazine, more than fifty thousand readers reported, ‘There is no possible way.’ Yet it is a very simple puzzle.
I’ll withhold the answer.
A puzzle from Russia:
Draw two straight lines on the clock face so that the sums of the numbers in each part are equal.
Four missiles are located in the corners of a square 20 miles on each side. All are launched simultaneously, and each homes in on the one on its left at 1 mile per second. How much time will pass before they meet?
From Lewis Carroll’s first textbook in symbolic logic:
- No kitten that loves fish is unteachable.
- No kitten without a tail will play with a gorilla.
- Kittens with whiskers always love fish.
- No teachable kitten has green eyes.
- No kittens have tails unless they have whiskers.
What conclusion can be drawn from these premises?
A bewildering riddle by the English statesman Charles James Fox (he of the widely spaced aunts):
I went to the Crimea; I stopped there, and I never went there, and I came back again. What am I?
Well, you’ve gone and murdered someone again. And this time you’ve done it in Elephantistan, which is renowned for its peculiar justice system.
The jury is divided, so you will decide your own fate. You’re presented with two urns, each of which contains 25 white balls and 25 black ones. Blindfolded, you must choose an urn at random and then draw a ball from it; a black ball means death, but a white one means you go free.
Tradition gives you the option to distribute the balls however you like between the two urns before you don the blindfold. This is thought to be a formality, as the total proportion of white balls to black does not change.
What should you do?
A riddle by Jonathan Swift:
By something form’d, I nothing am,
Yet everything that you can name;
In no place have I ever been,
Yet everywhere I may be seen;
In all things false, yet always true,
I’m still the same–but ever new.
Lifeless, life’s perfect form I wear,
Can shew a nose, eye, tongue, or ear,
Yet neither smell, see, taste, or hear.
All shapes and features I can boast,
No flesh, no bones, no blood–no ghost:
All colours, without paint, put on,
And change like the cameleon.
Swiftly I come, and enter there,
Where not a chink lets in the air;
Like thought, I’m in a moment gone,
Nor can I ever be alone:
All things on earth I imitate
Faster than nature can create;
Sometimes imperial robes I wear,
Anon in beggar’s rags appear;
A giant now, and straight an elf,
I’m every one, but ne’er myself;
Ne’er sad I mourn, ne’er glad rejoice,
I move my lips, but want a voice;
I ne’er was born, nor e’er can die,
Then, pr’ythee, tell me what am I?
In a 1999 quiz, the Washington Post asked its readers, “What automobile is referred to in a license plate that reads 1 DIV 0?”
The winning answer came from Supreme Court chief justice William Rehnquist, of all people. What was it?
Montana, Wyoming, and South Dakota meet at one point. Maryland, Virginia, and the District of Columbia meet at two — at Washington’s westernmost and southermost points along the Potomac River.
Name three U.S. states all three of which meet at three different points.