### #1 - Glass Problem

Given three bowls: 7, 4 and 3 liters capacity. Only the 7-liter is full. Pouring the water the fewest number of times, make the quantities of 2, 2, and 3 liters.

Three numerals in each number stand for litres in each bowl:
700 - 340 - 313 - 610 - 601 - 241 - 223 (overspilling 6 times)

### #2 - Number Problem

I just found a number with an interesting property:
When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.
It's not a small number, but it's not really big, either. When I looked for a smaller number with this property I couldn't find one.
Can you find it?

2519

### #3 - 3 RapidFire Problem

1.what gets hotter as it gets colder?
2.what is white when it's dirty turns black as you clean it?
3.what gets wetter as it dries?

1.what gets hotter as it gets colder?
The fireplace as winter approaches

2.what is white when it's dirty turns black as you clean it?
Blackboard

3.what gets wetter as it dries?
Towel

### #4 - Honestants and Swindlecants Problem

On this mysterious island there are 2 kinds of people - Honestants who always make true statements and Swindlecants who always make false statements.
In the pub the gringo met a funny guy who said: 'If my wife is an Honestant, then I am Swindlecant.' Who is this couple?

In this logical conditional (if-then statement) p is a hypothesis (or antecedent) and q is a conclusion (or consequent).
It is obvious, that the husband is not a Swindlecant, because in that case one part of the statement (Q)  ... then I am Swindlecant. would have to be a lie, which is a conflict. And since A is an Honestant, the whole statement is true.
If his wife was an Honestant too, then the second part of statement (Q)  ... then I am Swindlecant. would have to be true, which is a conflict again. Therefore the man is an Honestant and his wife is a Swindlecant.

### #5 - Tennis Ball

Given 27 table tennis balls, one is heavier than the others.
What is the minimum number of weighings (using a two-pan balance scale) needed to guarantee identifying the heavy one? Always. Of course, the other 26 balls weigh the same.

It is enough to use a pair of scales 3 times.
Divide the 27 balls to 3 groups, 9 balls in each. Compare 2 groups  the heavier one contains the ball. If there is equilibrium, then the ball is in the third group. Thus we know the 9 suspicious balls.
Divide the 9 balls to 3 groups of 3. Compare 2 groups, and as mentioned above, identify the group of 3 suspicious balls.
Compare 2 balls (of the 3 possibly heavier ones) and you know everything.
So we used a pair of scales 3 times to identify the heavier ball.

### #6 - Trip Problem

If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip?

average speed = total distance / total time
60 = 60 / (1 + 30/r)
60(1+ 30/r) = 60
1 + 30/r = 1
30/r = 0
Which is impossible. (The rate of the second half cannot be 0)

### #7 - 6 Cup 1 move Problem

Here are six cups. Three of them are empty, three have wine in them. Your goal is to make the line of cups alternate (wine-empty-wine-empty or empty-wine-empty-etc). You can only touch one cup and that is the cup you move. You may not move any other cups with or without your hand except if you are pushing the cup you chose to move between two other cups. How do you do it?

Pour cup 4 into empty cup 1!

### #8 - CAT EXAM ProbleM

5+3+2 = 151022

9+2+4 = 183652

8+6+3 = 482466

5+4+5 = 202541

THEN ;

7+2+5 =

7*2 , 7*5 , 7*2 + 7*5 -2

### #9 - Tanya Date

Tanya wants to go on a date and prefers her date to be tall, dark and handsome.
Of the preferred traits - tall, dark and handsome - no two of Adam, Bond, Cruz and Dumbo have the same number.
Only Adam or Dumbo is tall and fair.
Only Bond or Cruz is short and handsome.
Adam and Cruz are either both tall or both short.
Bond and Dumbo are either both dark or both fair.
Who is Tanya's date?

Cruz is Tanya's date.
As no two of them have the same number of preferred traits - from (1), exactly one of them has none of the preferred traits and exactly one of them has all the preferred traits.

From (4) and (5), there are only two possibilities:
* Adam & Cruz both are tall and Bond & Dumbo both are fair.
* Adam & Cruz both are short and Bond & Dumbo both are dark.

But from (2), second possibility is impossible. So the first one is the correct possibility i.e. Adam & Cruz both are tall and Bond & Dumbo both are fair.

Then from (3), Bond is short and handsome.

Also, from (1) and (2), Adam is tall and fair. Also, Dumbo is the person without any preferred traits. Cruz is Dark. Adam and Cruz are handsome. Thus, following are the individual preferred traits:

Cruz - Tall, Dark and Handsome
Adam - Tall and Handsome
Bond - Handsome
Dumbo - None :-(

Hence, Cruz is Tanya's date.

### #10 - wherz dad Problem

Right now mum is 21 years older then her child. in 6 years her child will be 5 times younger than she.
Q: where is daddy?

on top of mom