## 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

How do you make the number 7 an even number without addition, subtraction, multiplication, or division?

Drop the "S".

the answer

What do you get when you cross a cow with a trampoline?

A milkshake.

the answer

An intelligent trader travels from one place to another with 3 sacks having 30 coconuts each. No sack can hold more than 30 coconuts. On the way, he passes 30 check points. At each check point, he has to give one coconut for every sack he is carrying. What is the maximum number of coconuts that he can have with him at the end of his journey?

He will have 25 coconuts with him at the end. The trick is to reduce the number of sacks as you pass checkpoints. The first 10 checkpoints require 3 coconuts each, which empties his first sack. The next 15 checkpoints require 2 coconuts each, which will empty his second stack. Now, he is left with 1 sack and 5 more checkpoints. So, the 5 checkpoints will take 1 coconut each. Therefore, he will be left with 25 coconuts.

the answer

It is young but not that old. It gives you money. What is it?

Your mom.

the answer

You and a friend are standing in front of two houses. In each house lives a family with two children.
"The family on the left has a boy who loves history, but their other child prefers math," your friend tells you.
"The family on the right has a 7-year old boy, and they just had a new baby," he explains.
"Does either family have a girl?" you ask.
"I'm not sure," your friend says. "But pick the family that you think is more likely to have a girl. If they do have a girl, I'll give you $100."
Which family should you pick, or does it not matter?

You should pick the house on the left. Specifically, there is a 2/3 chance that the family on the left has a girl, whereas there's only a 1/2 chance that the house on the right has a girl.
This is a very counterintuitive riddle. It seems like there should always be a 1/2 chance that a given child is a girl. And in fact there is. The key word there is "given". Because we are not asking about a "given" child for the house on the left. We are asking about what could be either child. Whereas for the house on the right, we are asking about a "given" child...specifically, we're asking about the younger child.
There are 3 possibilities for the children in the first house:
Younger Older
Girl Boy
Boy Girl
Boy Boy
There is no "Girl, Girl" option because we know the house on the left has at least one boy. Since each of these 3 options is equally likely, and 2 of them have one girl, there is a 2/3 chance of there being a girl in the house on the left.
For the house on the right, because we already know the older child is a boy, there are only two possibilities:
Younger Older
Girl Boy
Boy Boy
And as we can see, there is a 1/2 chance for the house on the right having a girl.

the answer

I am small and shy.
I have eight legs.
I eat bugs.
I catch them in my web.
I am a...

Spider.

the answer

What do you call a cat crossed with a fish?

Catfish.

the answer

I move very slowly at an imperceptible rate, although I take my time, I am never late. I accompany life, and survive past demise, I am viewed with esteem in many women's eyes. What am I?

I am your hair.

the answer

I repeat only the last word you say. The more I repeat, the softer I got. I cannot be seen but can be heard. What am I?

An Echo.

the answer

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