## Really hard algebra puzzle

2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=?
Solve it?

98
2+3=2*[3+(2-1)]=8
3+7=3*[7+(3-1)]=27
4+5=4*[5+(4-1)]=32
5+8=5*[8+(5-1)]=60
6+7=6*[7+(6-1)]=72
therefore
7+8=7*[8+(7-1)]=98
x+y=x[y+(x-1)]=x^2+xy-x

the answer

2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=?
Solve it?

98
2+3=2*[3+(2-1)]=8
3+7=3*[7+(3-1)]=27
4+5=4*[5+(4-1)]=32
5+8=5*[8+(5-1)]=60
6+7=6*[7+(6-1)]=72
therefore
7+8=7*[8+(7-1)]=98
x+y=x[y+(x-1)]=x^2+xy-x

the answer

I am a mother and a father, but have never given birth. I'm rarely still, but I never wander. What am I?

Tree.

the answer

Which is the smallest number that you can write using all the vowels exactly once?

fIvE thOUsAnd (5000).

the answer

The thunder comes before the lightning; the lightning comes before the clouds. The rain dries everything it touches.

A volcano.

the answer

A teacher decides to give a pop quiz one day but all of her students refuse to take the quiz thinking that the teacher will call off the quiz. She can give only one of these students a detention for skipping the quiz. All of the students know each other’s names and if a student knows he/she is getting a detention they take the quiz.
How can she threaten her students with the single detention so they all take the quiz?

She tells them that she will give the student who skips the quiz whose name comes first alphabetically a detention. This student won’t skip because they know they are getting a detention if they do. The next person alphabetically will then know that they will get a detention so they won’t skip either, and so on.

the answer

Why is 6 afraid of 7?

Because seven was hungry and 'seven ate nine' (7, 8, 9).

the answer

Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).
They grow 12 different varieties.
Everybody grows exactly 4 different varieties
Each variety is at least in one garden.
Only one variety is in 4 gardens.
Only in one garden are all 3 kinds of crops.
Only in one garden are all 4 varieties of one kind of crops.
Pears are only in the two border gardens.
Paul's garden is in the middle with no lily.
Aster grower doesn't grow vegetables.
Rose grower doesn't grow parsley.
Nuts grower has also gourd and parsley.
In the first garden are apples and cherries.
Only in two gardens are cherries.
Sam has onions and cherries.
Luke grows exactly two kinds of fruit.
Tulips are only in two gardens.
Apples are in a single garden.
Only in one garden next to the Zick's is parsley.
Sam's garden is not on the border.
Hank grows neither vegetables nor asters.
Paul has exactly three kinds of vegetable.
Who has which garden and what is grown where?

the answer

There is a row of five different color houses. Each house is occupied by a man of different nationality. Each man has a different pet, prefers a different drink, and smokes different brand of cigarettes.
The Brit lives in the Red house.
The Swede keeps dogs as pets.
The Dane drinks tea.
The Green house is next to the White house, on the left.
The owner of the Green house drinks coffee.
The person who smokes Pall Mall rears birds.
The owner of the Yellow house smokes Dunhill.
The man living in the centre house drinks milk.
The Norwegian lives in the first house.
The man who smokes Blends lives next to the one who keeps cats.
The man who keeps horses lives next to the man who smokes Dunhill.
The man who smokes Blue Master drinks beer.
The German smokes Prince.
The Norwegian lives next to the Blue house.
The man who smokes Blends has a neighbour who drinks water.
Who has fish at home?

German.

the answer

There are 5 ships in a port.
The Greek ship leaves at six and carries coffee.
The ship in the middle has a black chimney.
The English ship leaves at nine.
The French ship with a blue chimney is to the left of a ship that carries coffee.
To the right of the ship carrying cocoa is a ship going to Marseille.
The Brazilian ship is heading for Manila.
Next to the ship carrying rice is a ship with a green chimney.
A ship going to Genoa leaves at five.
The Spanish ship leaves at seven and is to the right of the ship going to Marseille.
The ship with a red chimney goes to Hamburg.
Next to the ship leaving at seven is a ship with a white chimney.
The ship on the border carries corn.
The ship with a black chimney leaves at eight.
The ship carrying corn is anchored next to the ship carrying rice.
The ship to Hamburg leaves at six.
Which ship goes to Port Said? Which ship carries tea?

The French ship.

the answer

1
11
21
1211
111221
312211
What is the next number in the sequence?

The next number it: 13112221. Each number describes the previous number. Starting with 1, the second line describes it 11 (one 1). Then the third line describes 11 as 21 (two 1’s). Then the fourth line describes 21 as 1211 (one 2, one 1). This is the pattern.

the answer

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