The six friends are called John, Jack, James, Tuesday, Wednesday, and Thursday. John, Jack, James, and Tuesday cooked the mushrooms. Wednesday joined them and they ate the mushrooms. Thursday was the one to find them dead, so he is the survivor.

Simply roll the two cylinders on the ground. The hollow one will roll farther than the solid one since it will have a higher moment of inertia.

You can take the two horizontal matchsticks from the first 0, form the number 11 with them to get 1100011. You can also make 1111000 if you don’t mind that the power’s font is larger than the base’s font, or use the quite uncommon operation “tetration” to get 1111000.

The solution is shown below.

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 are not among the fastest 3.
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.

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.

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.

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.

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.

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