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If you hang a painting over two nails on the wall and remove one of the nails, the string of the painting will stay over the other nail, and the painting will keep hanging. Can you wrap a string around the nails in such a way, so that after removing any of the nails, the painting will fall?
The solution is shown below.
There are 25 horses and you want to find the fastest 3 among them. You can race any 5 of the horses against each other and see the final standing, but not the running times. If all the horses have constant, permanent speeds, how many races do you need to organize in order to find the fastest 3?
Let us label the horses H1, H2, H3, H4, …, H24, H25.
We race H1 – H5 and (without loss of generality) find that H1 > H2 > H3 > H4 > H5. We conclude that H4, H5
We race H6 – H10 and (without loss of generality) find that H6 > H7 > H8 > H9 > H10. We conclude that H9, H10 are not among the fastest 3.
We race H11 – H15 and (without loss of generality) find that H11 > H12 > H13 > H14 > H15. We conclude that H14, H15 are not among the fastest 3.
We race H16 – H20 and (without loss of generality) find that H16 > H17 > H18 > H19 > H20. We conclude that H19, H20 are not among the fastest 3.
We race H21 – H25 and (without loss of generality) find that H21 > H22 > H23 > H24 > H25. We conclude that H24, H25 are not among the fastest 3.
We race H1, H6, H11, H16, H21 and (without loss of generality) find that H1 > H6 > H11 > H16 > H21. We conclude that H16, H21 are not among the fastest 3.
Now we know that H1 is the fastest horse and only H2, H3, H6, H7, H11 could complete the fastest three. We race them against each other and find which are the fastest two among them. We complete the task with only 7 races in total.
How many places are there on Earth so that if you travel 1 mile South, followed by 1 mile East, followed by 1 mile North, you will get back where you started from?
Remark: You can assume Earth is a perfect globe.
The answer is infinitely many. Of course, the North Pole is one such place. However, if you start close to the South Pole, such that after traveling 1 mile South you land on a parallel with total length of 1/N miles, N-integer number, then when traveling East you will encompass this parallel exactly N times and later will get back to the starting place. These are all places with the property described above.
A few days ago, my girlfriend broke up with me. We were never really right for one another, and I knew it was coming, but of course
At first I didn’t know how to respond, but eventually I decided to simultaneously take the high road and the low road. So I sent her this email:
Baby,
I’m sad your leaving.
I can’t believe we ended up here, after what was an wonderful beginning. I know at times things were good and at times they were badly, but I always thought we would make it.
I remember the start. Right when I saw you, I knew you were a people of interest.
Things were great for so long. But now, we all know whom is at fault, so I understand your decision.
The dogs are upset. Sandy just lays down looking sad and misses u. So does Rusty. They makes me feel better at least. I’m glad the shelter gave them to you and I.
I feel nauseous without you—I feel like I could throw up any second—but I understand. This is the way things had to be.
Hears what I want you too do: live your life, be happy, and be goode.
By 4ever,
–Dan
And I smiled smugly to myself. I knew that she would never understand what I was really saying. Do you?
In the text there are some words which are written incorrectly:
Baby,
I’m sad your leaving.
I can’t believe we ended up here, after what was an wonderful beginning. I know at times things were good and at times they were badly, but I always thought we would make it.
I remember the start. Right when I saw you, I knew you were a people of interest. Things were great for so long. But now, we all know whom is at fault, so I understand your decision.
The dogs are upset. Sandy just lays down looking sad and misses u. So does Rusty. They makes me feel better at least. I’m glad the shelter gave them to you and I.
I feel nauseous without you—I feel like I could throw up any second—but I understand. This is the way things had to be.
Hears what I want you too do: live your life, be happy, and be goode.
By 4ever,
–Dan
If you take these words, and correct the mistakes, you will get:
You’re a bad person who lies. You make me nauseated. Here’s to good bye forever.
A man must mail a precious necklace to his wife, but anything sent through the mail will be stolen unless it is sent in a padlocked box. A box can bear any number of padlocks, but neither of the spouses has the key to a lock owned by the other. How can the husband mail the necklace safely to his wife?
The man can put a lock on the box and send it to his wife. Then she can put her own lock and send it back. Once the man receives the box, he can remove his lock and send the box once again to his wife. When she gets it, she can finally unlock the box using her own key.
On the picture, you can see an example of a wall made of 2×1 bricks. On the wall, there are 2 cracks, which are straight lines passing through the whole wall from top to bottom and from left to right, without intersecting any bricks.
Can you make the following walls without any cracks:
The solution for a 5×6 wall is shown below. However, if the wall has dimensions 6×6, it is impossible to build it without any cracks. Indeed, assume the wall does not have any cracks. Therefore every line passing through it must intersect 2, 4, or 6 bricks. Since there are in total 10 lines passing through the wall and each brick is intersected by exactly one of them, the total number of bricks must be at least 10 x 2 = 20 > 18. This yields a contradiction.
Can you find what the following abbreviations stand for?
24 H in a D = 24 Hours in a Day
26 L of the A = ???
7 D of the W = ???
7 W of the W = ???
12 S of the Z = ???
66 B of the B = ???
52 C in a P (W J) = ???
13 S in the U S F = ???
18 H on a G C = ???
39 B of the O T = ???
5 T on a F = ???
90 D in a R A = ???
3 B M (S H T R) = ???
32 is the T in D F at which W F = ???
15 P in a R T = ???
3 W on a T = ???
100 C in a R = ???
11 P in a F (S) T = ???
12 M in a Y = ???
13 is U F S = ???
8 T on a O = ???
29 D in F in a L Y = ???
27 B in the N T = ???
365 D in a Y = ???
13 L in a B D = ???
52 W in a Y = ???
9 L of a C = ???
60 M in a H = ???
23 P of C in the H B = ???
64 S on a C B = ???
9 P in S A = ???
6 B to an O in C = ???
1000 Y in a M = ???
15 M on a D M C = ???
24 H in a D = 24 Hours in a Day
26 L of the A = 26 Letters of the Alphabet
7 D of the W = 7 Days of the Week
7 W of the W = 7 Wonders of the World
12 S of the Z = 12 Signs of the Zodiac
66 B of the B = 66 Books of the Bible
52 C in a P (W J) = 52 Cards in a Pack (Without Jokers)
13 S in the U S F = 13 Stripes in the United States Flag
18 H on a G C = 18 Holes on a Golf Course
39 B of the O T = 39 Books of the Old Testament
5 T on a F = 5 Toes on a Foot
90 D in a R A = 90 Degrees in a Right Angle
3 B M (S H T R) = 3 Blind Mice (See How They Run)
32 is the T in D F at which W F = 32 Degrees is the Temperature in Fahrenheit at which Water Freezes
15 P in a R T = 15 Players in a Rugby Team
3 W on a T = 3 Wheels on a Tricycle
100 C in a R = 100 Cents in a Rand
11 P in a F (S) T = 11 Players in a Football (Soccer) Team
12 M in a Y = 12 Months in a Year
13 is U F S = 13 is Unlucky For Some
8 T on an O = 8 Tentacles on an Octopus
29 D in F in a L Y = 29 Days in February in a Leap Year
27 B in the N T = 27 Books in the New Testament
365 D in a Y = 365 Days in a Year
13 L in a B D = 13 Loaves in a Baker’s Dozen
52 W in a Y = 52 Weeks in a Year
9 L of a C = 9 Lives of a Cat
60 M in an H = 60 Minutes in an Hour
23 P of C in the H B = 23 Pairs of Chromosomes in the Human Body
64 S on a C B = 64 Squares on a Chess Board
9 P in S A = 9 Provinces in South Africa
6 B to an O in C = 6 Balls to an Over in Cricket
1000 Y in a M = 1000 Years in a Millennium
15 M on a D M C = 15 Men on a Dead Man’s Chest
Tools were stolen from a construction site. Max Mouse found footprints and a tire track, leading him to believe there were two thieves – one walking and the other riding a bike. Even though Slylock Fox believes both tracks are related to the robbery, he suspects there was only one thief. Why?
The tire track cannot be from a bike. The tracks were left by one thief pushing a wheelbarrow, full of stolen tools.
In London, many Underground tube stations have two escalators going up, but just one going down. Why?
This is because when people leave the train, they pack into groups, whereas when they go to catch the train, their flow is evener.
You are in a room with nothing else but two indistinguishable iron rods. You know that one of them is magnetized, how can you figure out which one?
Touch the middle of the first rod with the end of the second rod. If the two rods get attracted to each other, then the second one is the magnet. If not, then the first one is the magnet.
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