#1 - Ants Problem

Three ants are going up a hill, one behind the other. The last ant then says to the other ants, 'There is an ant behind me!'' How come?

1.They're marching up the hill backwards.
2. the ant was lying

#2 - Egg Problem

how can you tell a raw egg from a hard-boiled egg ?

If you spin a hard boiled egg and briefly stop it, it will stay stopped. Do the same to a raw egg and the yolk will keep it going.

#3 - Monkey Truth Problem

There are people and strange monkeys on this island, and you can not tell who is who (Edit: untill you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

A is a lying Monkey.
B is a lying Human.

#4 - Pool Problem

A swimming pool has four faucets. The first can fill the entire pool with water in two days, the second in three days, the third in four days, and the last one can fill the pool in 6 hours.
How long will it take to fill the pool using all 4 faucets together?

Because there are 24 hours in one day, in one hour fills the first tap 1/48, the second tap 1/72, the third tap 1/96 and the fourth tap fills 1/6 of the reservoir. That is all together (6+4+3+48) / 288 = 61/288. The reservoir will be full in 288/61 hours, which is 4 hours 43 minutes and about 17 seconds.

#5 - Pilot Problem

Lavesh was piloting a plane behind a car but was never able to overtake it. Why?

The car was in a merry go round.

#6 - Magnet Problem

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

You can hang the iron rods on a string and watch which one turns to the north (or hang just one rod).
Gardner gives one more solution: take one rod and touch with its end the middle of the second rod. If they get closer, then you have a magnet in your hand.
The real magnet will have a magnetic field at its poles, but not at its center. So as previously mentioned, if you take the iron bar and touch its tip to the magnet's center, the iron bar will not be attracted. This is assuming that the magnet's poles are at its ends. If the poles run through the length of the magnet, then it would be much harder to use this method.
In that case, rotate one rod around its axis while holding an end of the other to its middle. If the rotating rod is the magnet, the force will fluctuate as the rod rotates. If the rotating rod is not magnetic, the force is constant (provided you can keep their positions steady).

#7 - Birthday Problem

The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?

He was born on December 31st and spoke about it on January 1st.

#8 - Mathematical Fraction Problem

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

473816952 if rounding changes the next numeral character

#9 - Mathematical Fraction Problem

Using four sevens (7) and a one (1) create the number 100. Except the five numerals you can use the usual mathematical operations (+, -, x, :), root and brackets ()

100 = 177-77 = (7+7)x(7+(1:7))

#10 - Mathematical Fraction Problem

Rectify the following equality 101 - 102 = 1 by moving just one digit.

101 - 102 = 1.