Puzzles

Between the Lines

From a 19th-century British broadside:

Madam,

The love and tenderness I have hitherto expressed to
you is false, and I now feel that my indifference towards
you increases every day, and the more I see you the more
you appear ridiculous in my eyes, and contemptible–
I feel inclined and in every respect disposed and determined
to hate you. Believe me I never had any inclination
to offer you my hand. Our last conversation I assure you
left a tedious and wretched insipidity which has not
possessed me with an exalted opinion of your character,
your inconstant temper would make me miserable,
and if ever we are united, I shall experience nothing but
the hatred of my parents, added to everlasting dis-
pleasure in living with you. I have a true heart to bestow,
but however I do not wish you for a moment to think
it is in your service, as I could not give it to one more
inconstant and capricious than yourself, and one less
capable to do honour to my choice, and my family.
You, Madam, I beg and desire will be persuaded that I
think seriously, and you will do me a great favour to
avoid me. I shall excuse you taking the trouble to
give me an answer to this, as your letters are full of
nonsense and impertinence, and have not a shadow of
wit and good sense. Adieu, and believe me truly, I am
so averse to you, that it is impossible I should ever be,
Madam, your Affectionate Servant and Lover, R.G.

“By reading every other line of the above letter the true meaning will be found out.”

The Absent King

smullyan - absent king

Raymond Smullyan devised this puzzle in 1957 while a student at the University of Chicago. The white king has just been knocked off the board during a legal game. Where was it standing?

Click for Answer

Five Down

From Henry Dudeney:

A banker in a country town was walking down the street when he saw a five-dollar bill on the curb. He picked it up, noted the number, and went to his home for luncheon. His wife said that the butcher had sent in his bill for five dollars, and, as the only money he had was the bill he had found, he gave it to her, and she paid the butcher. The butcher paid it to a farmer in buying a calf, the farmer paid it to a merchant who in turn paid it to a laundry woman, and she, remembering that she owed the bank five dollars, went there and paid the debt.

The banker recognized the bill as the one he had found, and by that time it had paid twenty-five dollars worth of debts. On careful examination he discovered that the bill was counterfeit. What was lost in the whole transaction, and by whom?

Click for Answer

Hand Count

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.

Click for Answer

“The Eiffel Tower”

http://farm5.static.flickr.com/4031/4481822987_b44803ddd0_o.png" alt="http://books.google.com/books?id=CpgkAQAAIAAJ&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q=&f=false

By C.W. Wood. White to mate in two moves.

Click for Answer

Hate Mail

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.

Click for Answer

A Little Crusade

http://books.google.com/books?id=HRRBAAAAYAAJ&pg=PA134&dq=chess+curiosities&as_brr=4&ei=e_uzS8KSMY3mygTujrjfCw&cd=1#v=onepage&q=chess%20curiosities&f=false

White to move his king only and mate in six moves.

Click for Answer

When in Rome

What number comes next in this series?

0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, 55, 1, 0, 1

Click for Answer

Road Work

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?

Click for Answer

Menagerie

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?

Click for Answer

“Four Puzzles in One”

http://books.google.com/books?id=YbcvAAAAMAAJ&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q=&f=false

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.

Click for Answer

Mate in Two

http://books.google.com/books?id=CpgkAQAAIAAJ&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q=&f=false

By G.A.A. Walker. White to play and checkmate all six black kings simultaneously with his second move.

Click for Answer

A Mysterious Windfall

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?

Erin Go

Count these leprechauns:

vanishing leprechaun 1

Now swap the two upper panels and count again:

vanishing leprechaun 2

Where has the extra one been hiding?

Hidden in Sight

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?

Click for Answer

Cornered

One of Eduard Gufeld’s first chess coaches, A.A. Olshansky, offered him this problem:

 src="http://farm5.static.flickr.com/4050/4438740010_4a22a1732e_o.png" alt="" /></p>

“White to mate in half a move.”

Click for Answer

A Curious Exchange

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?

Click for Answer

The Canals on Mars

http://books.google.com/books?id=QCy6DzgqcI4C&pg=PA66&lpg=PA66&dq=loyd+mars+%22there+is+no+possible+way%22&source=bl&ots=IDuPPpyYDz&sig=9jj5lsIGw5__uPt-2tPXRd8ZgzM&hl=en&ei=YgxVS_WKDtGXtgf82MWtDA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBQQ6AEwAw#v=onepage&q=&f=false

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.

Equal Time

http://www.flickr.com/photos/monkeyc/322654818/

Image: Flickr

A puzzle from Russia:

Draw two straight lines on the clock face so that the sums of the numbers in each part are equal.

Click for Answer

Arms Race

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?

Click for Answer

Claws and Effect

From Lewis Carroll’s first textbook in symbolic logic:

  1. No kitten that loves fish is unteachable.
  2. No kitten without a tail will play with a gorilla.
  3. Kittens with whiskers always love fish.
  4. No teachable kitten has green eyes.
  5. No kittens have tails unless they have whiskers.

What conclusion can be drawn from these premises?

Click for Answer

What Am I?

http://commons.wikimedia.org/wiki/File:Charles_James_Fox01.jpg

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?

Escape From Elephantistan

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?

Click for Answer

What Am I?

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?

Click for Answer