by Peter Keyne
This puzzle pushes possibility to its limits.
Today is Emilio’s birthday. His older twin sister, Elisa, telephones to wish him many happy returns. Three days later it is Elisa’s birthday, and this time it is Emilio’s turn to call and wish her a happy birthday.
How is it possible that Emilio and Elisa, though twins, have their birthdays three days apart?
Answers: Round 17
1. The most equitable division is to give the contributor of 5 loaves 7 pieces of silver, and the other man just 1. We should imagine the 8 loaves divided into thirds. If each man ate 1 third of each loaf of bread, they each had 8 thirds of the total 24 thirds.
The contributor of 5 loaves provided 15 of the total 24 thirds. If he had 8 himself, it means he provided 7 for the traveler. The contributor of 3 loaves, provided 9 of the total 24 thirds. If he had 8 himself, it means he provided only 1 for the traveler. Hence the division of 7 coins to 1 coin.
2. Four girls and three boys (the narrator must be a girl)
3. When they meet, they will be exactly the same distance from San Francisco.
4. Turn over both hourglasses. When the sand stops running in the 7-minute hourglass, turn it immediately back over. When the sand stops running in the 11-minute hourglass, turn the 7-minute hourglass over again. When the sand runs out of the 7-minute hourglass, exactly 15 minutes will have passed.
5. The jeweller can join all of the chains by breaking only five links. He should completely dismantle one of the chains, and then use the loose links to connect the other five chains into a necklace. Therefore the woman should only pay $5.
6. Yes, you should switch doors. If you switch doors, you will have a two in three chance of winning the car. If you do not switch, you will retain the one in three chance you began with. This has proved one of the most contentious puzzles of all time, and many people continue to argue that switching doors will have no impact on your chances of winning. They are wrong.
The car could be located behind door A, B, or C. We do not know where it will be, but will imagine for now that it is behind door A.
There are then three possible scenarios
1. The car is behind door A. You pick door A.
2. The car is behind door A. You pick door B.
3. The car is behind door A. You pick door C.
After you have chosen a door, the host, who knows what is behind each door, will reveal a goat.
1. The car is behind door A. You pick door A. Host reveals a goat behind door B or C.
2. The car is behind door A. You pick door B. Host reveals a goat behind door C.
3. The car is behind door A. You pick door C. Host reveals a goat behind door B.
You are now given an opportunity to switch doors
1. The car is behind door A. You pick door A. Host reveals a goat behind door B or C. Switching loses.
2. The car is behind door A. You pick door B. Host reveals a goat behind door C. Switching wins.
3. The car is behind door A. You pick door C. Host reveals a goat behind door B. Switching wins.
Switching doors wins in two of the three possible scenarios when the car is behind door A.
If the car is behind door B, or C, switching doors will also win in two of the three scenarios (you should explode the scenarios in full as we have done if you wish to check)
Another way of seeing things
The problem can also be viewed like this:
When you first pick a door, there is a one in three chance that you have chosen a car, and a two in three chance that you have chosen a goat. The odds are not in your favor. You know however, that the host is about to reveal a goat from behind one of the other two doors. What would you say if before revealing the goat, he offered you a chance to switch your one door for both of the others? You would certainly accept, as this would reverse the odds, and you would have a two in three chance of winning the car. The host effectively makes you this very offer. Before he opens the door with the goat behind it, we know exactly what he is going to do, and revealing it doesn’t cost us anything. In effect, we are offered whatever is behind both of the doors.
7. Take the following steps:
1. Fill the 5-gallon container.
2. Pour the water from the 5-gallon container into the 3-gallon container. (2 gallons remain in the 5-gallon container)
3. Empty the 3-gallon container.
4. Pour the 2 gallons from the 5-gallon container into the 3-gallon container.
5. Fill the 5-gallon container.
6. Finally, pour the water from the 5-gallon container into the 3-gallon container until it is full, and you are left with exactly 4 gallons in the 5-gallon container.
8. The prisoners agree that whoever is standing at the back of the line, in tenth position, will say “white” if he can see an odd number of white hats, and “black” if he can see an even number of white hats. The prisoner in tenth position cannot improve or reduce his own chances of being set free, but he can convey crucial information to the nine prisoners in front of him.
If the tenth prisoner says “white”, and the ninth prisoner sees an odd number of white hats in front of him, he knows that his own hat must be black — otherwise the tenth prisoner would have seen an even number of white hats. Equally, if the ninth prisoner sees an even number of white hats in front of him, he knows that his own hat must be white — otherwise the tenth prisoner would have seen an even number of white hats.
This explains how the ninth prisoner might correctly deduce the color of his hat through logical reasoning on his own part. Each successive prisoner will need to reason in a similar manner, but they do not have to memorize all of the answers they hear.
The first time a prisoner guesses “white”, it signifies that an odd number of white hats is visible from the speaker’s perspective.
When the next prisoner says “white”, it must signify that an even number of white hats is visible from the speaker’s perspective.
Each time someone says “white”, the signification changes.
Knowing this, each prisoner is able to deduce the color of his own hat based on the number of times he hears the prisoners behind him say “white”, and the number of white hats he can see in front of him.
This plan guarantees that nine of the prisoners will be set free. The prisoner at the back of the line, who speaks first, can never have more than a 50-50 chance of being set free.
9. 99 days
10. The twins’ mother went into labor while traveling by boat across a change of time zone. Elisa was born early on March the 1st. Emilio was born in a different time zone, in the late hours of February 28th. In most years, Emilio will therefore celebrate his birthday one day before his older sister celebrates hers. In leap years, Emilio will celebrate his birthday two days before his sister. And in the particular leap year in question, we must conclude that the twins are living on either side of the International Date Line. Let us say that Emilio is in Japan and Elisa is in the US. When she calls, it is the morning of February 28th in Japan, but still the evening of February the 27th in the US. Three days later, on the morning of March the 2nd in Japan, Emilio calls Elisa to wish her a happy birthday. It is the evening of March the 1st in the US.
*Illustrations
Round 18: Plain Ridiculous!
The ten puzzles in this round all share an element of the absurd and exist somewhere on the boundary between riddles and jokes. We would advise against spending too much time puzzling them out!
1. Insomnia
How is it possible for a person to go eight days in a row without sleeping?
2. Heavy Rain
A man walks two miles under heavy rain on an open road. He doesn’t have a hat, or hood, or umbrella, or anything else in fact with which to cover his head. And yet somehow, his hair doesn’t get wet.
How is this possible?
3. Take Five
How many times can you take 5 from 25?
4. Imprisonment
When you awake
, you find that you have somehow been transported to a room without any windows or doors. The walls, the ceiling and the floor are made of impenetrable stone. There is no equipment in the room to help you escape, and yet you manage to do so. How?
5. Nine Days a Week
Can you name four days which start with the letter 'T'?
6. A New Traffic Light
In which situation do you start at red and stop at green?
7. Anatomical Anomaly?
What word describes a woman who does not have all her fingers on one hand?
8. A Riddle by Lewis Carroll
John gave his brother James a box:
About it there were many locks.
James woke and said it gave him pain;
So gave it back to John again.
The box was not with lid supplied,
Yet caused two lids to open wide:
And all these locks had never a key
What kind of a box, then, could it be?
9. East Asian Cuisine
Why do Chinese men eat more rice than Japanese men?
10. An Unsolved and Probably Unsolvable Riddle by Lewis Carroll
Why is a raven like a writing desk?2
Answers: Round 18
1. By sleeping during the night.
2. The man is bald.
3. Once, the next time you’d be taking 5 from 20.
4. There are no doors, so you simply walk through the doorway.
5. Tuesday, Thursday, Tomorrow, Today
6. When you’re eating a watermelon
7. The phenomenon is so ordinary there isn’t a word for it. Like most people, the woman’s fingers are divided between two hands.
8. Here is Lewis Carroll’s own answer to the riddle:
As curly-headed Jemmy was sleeping in bed,
His brother John gave him a blow on the head;
James opened his eyelids, and spying his brother,
Doubled his fist, and gave him another.
This kind of box then is not so rare;
The lids are the eyelids; the locks are the hair,
And so every schoolboy can tell to his cost,
The key to the tangles is constantly lost.
9. Because there are considerably more Chinese men than Japanese men.
10. Your guess is as good as ours. Lewis Carroll said that he originally intended the riddle to be without an answer. Nonetheless, there have been a number of notable attempts to provide a satisfying answer. Puzzle expert, Sam Loyd, had the following to say:
My own guess, following the alliterative style which characterizes the entire work, would be “that the notes for which they are noted are not noted for being musical notes”; nevertheless, there is considerable scope for ingenuity and cleverness, as other answers, equally as good or better, might be suggested, like “because Poe wrote on both,” “Hills and tales are among their characteristics,” “Because they stand on their legs,” “Because they conceal their steels” or “Ought to be made to shut up,” etc., etc.
*Illustrations
Round 19: The Great Riddles from Literature
The first two riddles in this round were created by Jonathan Swift, the author of Gulliver’s Travels.
1. We Are Little Airy Creatures
We are little airy creatures,
All of different voice and features;
One of us in glass is set,
One of us you'll find in jet.
The other you may see in tin,
And the fourth a box within.
If the fifth you should pursue,
It can never fly from you.
2. Ever Eating, Never Cloying
Ever eating, never cloying,
All-devouring, all-destroying,
Never finding full repast,
Till I eat the world at last.
The following riddles were created by J.R.R. Tolkien and appear in his book, The Hobbit.
3. What Has Roots as Nobody Sees
What has roots as nobody sees,
Is taller than trees,
Up, up it goes,
And yet never grows?
4. Thirty White Horses on a Red Hill
Thirty white horses on a red hill,
First they champ,
Then they stamp,
Then they stand still.
5. Voiceless it Cries
Voiceless it cries,
Wingless it flutters,
Toothless bites,
Mouthless mutters.
6. An Eye in a Blue Face
An eye in a blue face
Saw an eye in a green face.
"That eye is like to this eye"
Said the first eye,
"But in low place,
Not in high place."
7. It Cannot Be Seen, Cannot Be Felt
It cannot be seen, cannot be felt,
Cannot be heard, cannot be smelt.
It lies behind stars and under hills
And empty holes it fills.
It comes first and follows after,
Ends life, kills laughter.
8. A Box without Hinges, Key, or Lid
A box without hinges, key, or lid,
Yet golden treasure inside is hid.
9. Alive Without Breath
Alive without breath,
As cold as death;
Never thirsty, ever drinking,
All in mail never clinking.
10. No-legs Lay on One-leg
No-legs lay on one-leg, two-legs sat near on three-legs, four-legs got some.
11. This Thing All Things Devours
This thing all things devours:
Birds, beasts ,trees, flowers;
Gnaws iron, bites steel;
Grinds hard stones to meal;
Slays king, ruins town,
And beats high mountain down.
Answers: Round 19
1. The Vowels: A, E, I, O and U
2. Time
3. A Mountain
4. Teeth
5. Wind
6. The Sun Shining on Daisies
7. Darkness
8. An Egg
9. A Fish
10. It is a description of a man sitting on a stool with a fish on a plate in front of him. His cat gets the bones.
11. Time
*Illustrations
Round 20: Outside the Box
1. A Curious Purchase
A family goes to a hardware store, searching for something that will put the finishing touch to their new house. They find what they’re looking for and it’s priced as follows:
1 for $1
10 for $2
100 for $3
They buy 212 and are still charged only $3.
What did they buy?
2. Tunnelling Prisoners
A man is imprisoned in the king’s dungeon. The walls are made of stone and the oak door is permanently locked. High up on one of the walls is an unbarred window. There is no way of climbing the walls, and there is no furniture in the room that the man can stand on to reach it. The man abandons hope of escaping through it and decides to try and dig his way out. He makes slow progress and calculates that it will take his entire lifetime to tunnel out. For a few days he abandons this project as well. Suddenly an idea comes to the man, and he begins to dig again.
What is his plan?
3. Four Jolly Men — Another Puzzle by Sam Loyd
Four jolly men sat down to play,
And played all night till break of day.
They played for gold and not for fun,
With separate scores for every one.
Yet when they came to square accounts,
They all had made quite fair amounts!
Can you the paradox explain?
If no one lost, how could all gain?
4. Alike in all Things
Two girls are born to the same mother, on the same day, at the same time, in the same month and year, and yet they're not twins. How is this possible?
5. An Obstina
te Bird
A man buys a parrot from the Great Bazaar. The merchant promises him, “this parrot will repeat every word it hears”. Over the following months, the man goes to great lengths to teach the bird to speak. It never says a single word, and yet the merchant was completely truthful. How is this possible?
6. The Bookworm
A three-volume novel rests on a bookshelf as pictured above. There are 300 pages in each volume. A bookworm has decided to make the neglected masterpiece its home. It tunnels from the first page of Volume I to the final page of Volume III.
Excluding the covers, how many pages does the bookworm tunnel through in total?
7. Inside the Box
Three closed boxes containing marbles are placed in front of you. They are labelled: “black marbles”, “white marbles”, and “both black and white marbles”. However, you know that someone has mischievously switched all of the labels.
If you are only allowed to reach into one box, and remove one marble, which box should you choose in order to determine the contents of all three boxes?
8. Death Sentence
A statesman was sentenced to exile, and his political opponents were keen that the sentence be upheld. The custom of the land however, was to let fate determine the finality of such sentences. Two slips of paper would be placed into a jar, and the statesman asked to select one of them. One of the slips would be marked “Exile”, and the other “Pardon“.
