by Peter Keyne
2. A Little House
Is it possible to draw the house below without lifting your pen from the paper, and without going over any of the lines more than once?
3. The Clever Gardener
A gardener is asked to plant five rows of cherry trees with four trees in each row. His employer gives him exactly enough money to buy twenty trees from the local nursery, and jokingly tells him that he can keep whatever change there is. On the way to the nursery, the gardener realizes that it if he buys just ten trees, it will still be possible to plant five rows with four trees in each, and he can keep half the money he has been given.
How does he plan to plant the trees?
4. Number Grid 1-9
How can you place the numbers 1-9 in a 3x3 grid so that every horizontal, vertical and diagonal line adds up to 15?
5. Nine Minus Three
By drawing one continuous line,
Can you subtract three from this nine?
IX
6. Clock Face Division
How can you divide a clock face into three parts, so that the sums of the numbers in each part are equal?
7. Tic-Tac-Toe
What is the maximum number of X’s you can place on a Tic-Tac-Toe board, without making three-in-a-row in any direction?
8. Two Ways
How can you add just one straight line to this equation to make it correct?
9. Nine Dots; Four Lines
The challenge here is to connect the nine dots using only four straight lines, and without lifting your pen from the paper.
10. Number Grid 1-8
How can you place the numbers 1-8 in the grid below, so that no consecutive numbers are in bordering squares (horizontally, vertically, or diagonally)?
Answers: Round 13
1. It is a sequence of the numbers from 1-5 beside their mirror images.
2. Yes. Here is one of several possible solutions.
3. He will plant the trees in a five-point star formation.
4.
5. Draw an “S” in front of the IX, to convert it to “SIX”.
6. By this division, the sum of each part is 26.
7. Six:
8.
9.
Alternative solutions exist.
An origami-based solution makes it possible to align all of the dots and connect them with a single line. Equally, if the dots were drawn on a spherical object, it would be possible to draw a single straight line around the object that connected all of the dots.
10. Here is one possible solution.
*Illustrations
Round 14: What am I? New Riddles
The riddles included in this round have never been published before. We knew when we began compiling this collection that we wanted to include some completely original material, and decided that for this section, we would invite submissions from around the world. We were overwhelmed with the response. The following ten puzzles are our finest gleanings and come from five different countries. We hope you enjoy them.
Thank you and congratulations to the ten authors represented here.
1. Five Creatures Cross a Field of Snow
Five creatures cross a field of snow;
But leave a single track behind
Whose loops and bows are soon, I know,
Unravelled by the mind.
2. She Wears a Blue Ring
She wears a blue ring,
She wears a grey cloak.
She cannot sing her suffering
— Her tongue is made of oak.
3. It’s Clear These Three Are Brothers
It’s clear these three are brothers
For they share a single face.
But tell me why they chase each-other
Round and round their dwelling place.
4. Henry VIII to Anne Boleyn
“A gift?” “Yes love, a gift for you —
A vessel.” “Ah! for drinking wine?”
“No love, observe, wine passes through.
It is for flesh and blood — and thine!”
What is the gift?
5. Tonight at the Ball I Dance, I Dance
Tonight at the ball I dance, I dance
As well as any you see.
Yet nobody takes me by the hand,
Or says a word to me.
6. An Alien’s Instructions for Using an Artefact Discovered on Earth
To hypnotize, locate the eyes,
And drive your fingers through: Hold tight;
The mouth’s now yours; the teeth and jaws,
Speak not — but bite bite bite!
7. My Makers, Having Had Their Hour
My makers, having had their hour,
Depart. I gain a hat and power
And like an actor from the wings
Step out upon the stage of kings.
8. When You Walk on the Living
When you walk on the living, there’s scarcely a whisper;
But walk on the dead, and the crunch is much crisper!
The bones you have broken, are strewn in the street,
— What lies beneath your feet?
9. You Are Not Envious of Her
You are not envious of her,
Or so I’m sure you’d say,
But tell me why you always wear
What she wore yesterday?
Who is the mysterious woman?
10. Evening’s Softest Blanket’s Here
Evening’s softest blanket’s here
And brilliantly white.
And yet I pray to God I’m not
Enwrapped in it tonight!
Answers: Round 14
1. A Scribe’s Hand (Submitted by Deborah Jones from Tampa, Florida)
2. A Castle (Submitted by A. Gupta. from, Mumbai, India)
3. The Three Hands on a Clock Face (Submitted by Ellen Seares from, Auckland, New Zealand)
4. A Ring (Submitted by R. Hobbs from Bexhill, England)
5. A Shadow (Submitted by A. Franks from London, England)
6. A Pair of Scissors (Submitted by Immy Cooper from Dover, New Hampshire)
7. A Prince (Submitted by O. Emberey from Edinburgh, Scotland)
8. Fallen Leaves (Submitted by Luke Laycock from Manchester, England)
9. A Coat Hanger (Submitted by S. Taylor from Chicago, Illinois)
10. Fresh Snowfall (Submitted by I. Oliver, from New York)
*Illustrations
Round 15: Ditloids
This round presents ten “ditloids”, where the challenge is simply to decipher what each initial stands for.
Example: 24 H in a D = 24 hours in a day
1. 12 S on the F of the E U
2. 18 H on a G C
3. 2 W in a F
4. 7 H P B by J K R
5. 2 Q in a C
6. 7 E in the H
7. 1 H in a D
8. 16 O in a P
9. 1 M, 1 T, 1 W, 1 T, 1 F, 1 S, and 1 S in a W
10. 16 P, 4 K, 4 B, 4 R, 2 Q and 2 K in a G of C
Answers: Round 15
1. 12 Stars on the Flag of the European Union
2. 18 Holes on a Golf Course
3. 2 Weeks in a Fortnight
4. 7 Harry Potter Books by J. K. Rowling
5. 2 Quavers in a Crotchet
6. 7 Events in the Heptathlon
7. 1 Hole in a Doughnut
8. 16 Ounces in a Pound
9. 1 Monday, 1 Tuesday, 1 Wednesday, 1 Thursday, 1 Friday, 1 Saturday, and 1 Sunday in a Week
10. 16 Pawns, 4 Knights, 4 Bishops, 4 Rooks, 2 Queens and 2 Kings in a Game of Chess.
*Illustrations
Round 16: Number Puzzlers 2
1. Creative Subtraction
If you remove 1 from 10 the answer is 9. But how is it possible to remove 1 from 9 and get 10 as the answer?
2. Six digits in a Sum
How can you use each of the digits from 1-6 to complete the equation on the blackboard?
3. Seven Pairs of Gloves
Seven pairs of b
lack gloves and three pairs of brown gloves are mixed together in a box. If you were to reach into it blindfolded, how many gloves would you have to remove to be certain of having a matching pair?
4. Three and a Half Boys
A woman has seven children. Half of them are boys. How can this be possible?
5. A Seemingly Simple Sum
A teacher leans over one of her student’s desks and puts a big red cross beside one of his sums. The student protests that the sum is correct, and is able to prove it to his teacher very simply. What did he do?
6. Goats and Chickens
A farmer is happy to let his chickens and goats wander in the same field. More out of courtesy than interest, you ask him how many animals there are in the field in total. It pleases him to reply cryptically, and he tells you that there are 30 heads and 84 legs in the field.
Can you work out from this how many goats and how many chickens he has?
7. A Profitable Horse
An unusual business opportunity presents itself. You are offered an excellent horse for only $60 dollars. Naturally, you buy it. A year later, a stranger wishes to buy the horse, and offers you $70. With little concern for the animal’s feelings, you decide to part with it. Another year later, you see the horse again, and are filled with regret. It really is a fine animal. The stranger agrees to sell it back to you, but you have to pay him $80. Finally, another year later, you meet the original owner of the horse. He too regrets having parted with it, and agrees to pay $90 to get it back.
Who has profited most from the sale of the horse, and how much have they made?
8. Easy Addition
This puzzle works best when you read it aloud to someone else.
Perform the following calculation in your head, adding the numbers as quickly as you can. You may not use a pen and paper. Start with 1000 and add 40. Now add 1000. Add 30. Add another 1000. Now add 20. Add another 1000 and finally, add 10. What is the total?
9. Strange Addition
When is it possible to add 3 to 10 and get 1 as the answer?
10. Endless Addition
A misbehaving schoolboy receives an educational punishment from his maths teacher (who has always recognized the boy’s ability, but continues to question his attitude). He is asked to stay behind during break-time until he has added up all of the numbers from 1 to 50.
To the boy’s delight, and his teacher’s secret satisfaction, he calculates the answer in no time at all. The teacher challenges him to add the numbers from 1 to 1000, and he arrives at this answer almost as quickly as the first.
What calculation did he perform?
Answers: Round 16
1. Use Roman numerals: Nine (IX) minus one (I) = Ten (X)
2. 54x3 = 162
3. Eleven. In the worst possible scenario, you draw seven right-hand black gloves, and three right-hand brown gloves. The eleventh glove is certain to complete a pair.
4. They are all boys.
5. Turned his book around.
6. There are 12 goats and 18 chickens
The following line of reasoning can lead you to the answer:
G+C = 30
4G+2C = 84
2G +2C = 60
2G= 24
G=12
C=18
7. You have. You made a $20 dollar profit; the stranger made a $10 profit; and the original owner made a $30 loss.
8. 4100 (If you are only hearing the sum, it’s very easy to move from 4090 to 5000 when you add the final 10)
9. When you are telling the time.
10. The boy realized that the median (middle point) of the numbers he is asked to add will also be their mean (average). He can therefore calculate the sum by simply identifying the median and multiplying it by however many numbers he is asked to add.
If we add the numbers 1, 2, 3, 4, 5, we can see that the median is 3. This is also the mean of the numbers, and so when multiplied 5, it gives us the sum of the numbers, 15.
For the number 1-50, the boy takes a pen and paper and calculates 25.5 (the median and mean) x 50 = 1275
In the second instance, the sum is 500.5 x 1000 = 500500
*Illustrations
Round 17: Pure Logic 3
1. Eight Loaves of Bread
A hungry traveler approaches a roadside tent, where two men have spread a simple lunch and are about to begin eating. The men invite the traveler to join them, and he accepts their invitation on condition that they allow him to pay for his portion. He learns that one of his hosts has contributed five loaves of bread to the lunch, and the other three.
The three men consume equal shares of the eight loaves, and upon taking his leave the traveler lays down eight pieces of silver to pay for his share. The contributor of the five loaves takes five pieces of silver and leaves three to his partner, who objects to the division and insists on getting half of the money.
The traveler does not wish to intrude in their affairs, but has an idea of how the money might be more equitably divided.
How many pieces of silver should each of his hosts receive?
2. Brothers and Sisters
I have as many brothers as I have sisters, but each one of my brothers has twice as many sisters as he has brothers. How many boys and how many girls are we in total?
3. Train to New York
A train leaves San Francisco bound for New York City. The distance between the cities is approximately 3000 miles, and the train travels at 100mph. Two hours later, a train leaves New York City bound for San Francisco. It is a faster train and travels at 200mph.
When the trains meet, which of them will be closer to San Francisco?
4. Two Hourglasses
With a 7-minute hourglass and an 11-minute hourglass, what is the simplest way to time exactly 15 minutes?
5. Links in a Chain
A woman has six pieces of silver chain, each consisting of five links. She wishes to join the chains together to make a necklace, and visits a jeweller to inquire about the cost. He informs her that for every link he needs to break open and close again, he charges $1. How much must the woman pay to make the necklace?
6. The Monty Hall Problem
Imagine you are on a game show, and the host offers you a choice of three doors. Behind one door is a car, and behind each of the other two doors is a goat. You choose a door. Regardless of your choice of door, the show will then proceed as follows:
The host, who knows what is behind each of the doors, opens another door to reveal a goat. He then asks you whether you would like to switch from the door you originally chose to the other unopened door.
Is it to your advantage to switch doors?
7. Four Gallons of Water
It is a fine day and you are standing at the river bank with a 5-gallon container and a 3-gallon container. Both are irregularly shaped. Strangely, you resolve to enjoy the day by filling the 5-gallon container with exactly 4 gallons of water? How do you accomplish it?
8. Prisoners and Hats
A prison warden has resolved to give ten prisoners an opportunity to win their freedom.
Tomorrow, the men will be lined-up in single file, in a randomly determined order. They will all be facing in the same direction, and will only be able to see the people standing in front of them ( the tenth prisoner in the line will be able to see nine prisoners in front of him, whereas the first prisoner will not be able to see anyone).
The warden will then place either a black or a white hat on each prisoner’s head. He may choose any arrangement of black and white hats. There could be ten white hats and no black hats, or seven white hats and three black hats. The prisoners will only be able to see the color of the hats in front of them.
When all of the hats have been placed, the warden will walk to the back of the line and ask prisoner number ten: “What color hat are you wearing?” In reply, the prisoner may only say “black” or “white”. Aside from this, he may not in any way communicate with the other prisoners. If he replies correctly, he will be set free. If h
e replies incorrectly he will be shot. The warden will move down the line asking each prisoner the same question in turn.
The warden has agreed that the prisoners can meet together this evening to formulate a plan of action.
What plan will maximize the number of lives they can save?
9. The Sorcerer’s Tower
The sorcerer’s tower was enchanted in such a way that it was able to build itself. Bricks, slates, tiles, and panes of glass, all flew to it of their own accord and danced into position. The tower doubled in size every day until after 100 days it reached a height that provided fine views over the entire realm. How many days did the tower take to reach half its full height?
10. Twins Three Days Removed