3. General Gasslefield, accused of high treason, is sentenced to death by the court-martial. He is allowed to make a final statement, after which he will be shot if the statement is false or will be hung if the statement is true. Gasslefield makes his final statement and is released. What could he have said?

General Gasslefield said:
"I will be shot."
If this statement was true, he would have been hung and thus not be shot. But then his statement would be false, which implies that he should be shot, making the statement true again, etc... In other words: the verdict of the court-martial could not be executed and the general was released..

5. A snail is at the bottom of a 20 meters deep pit. Every day the snail climbs 5 meters upwards, but at night it slides 4 meters back downwards. How many days does it take before the snail reaches the top of the pit?

On the first day, the snail reaches a height of 5 meters and slides down 4 meters at night, and thus ends at a height of 1 meter. On the second day, he reaches 6 m., but slides back to 2 m. On the third day, he reaches 7 m., and slides back to 3 m. ... On the fifteenth day, he reaches 19 m., and slides back to 15 m. On the sixteenth day, he reaches 20 m., so now he is at the top of the pit! Conclusion: The snail reaches the top of the pit on the 16th day!... .

6. A cable, 16 meters in length, hangs between two pillars that are both 15 meters high. The ends of the cable are attached to the tops of the pillars. At its lowest point, the cable hangs 7 meters above the ground. How far are the two pillars apart?

Note that it is a kind of trick question: the pillars stand next to each other. Which means that the cable goes 8 meters straight down and 8 meters straight up. Conclusion: The distance between the pillars is zero meters..

8. Yesterday evening, Helen and her husband invited their neighbours (two couples) for a dinner at home. The six of them sat at a round table. Helen tells you the following: "Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna. Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband. Jim sat on the left of the woman who sat on the left of Roger. I did not sit beside my husband." What is the name of Helen's husband?

From the second statement, we know that the six people sat at the table in the following way (clockwise and starting with Helen's husband):
Helen's husband, woman, man, woman, man, Esther Because Helen did not sit beside her husband, the situation must be as follows: Helen's husband, woman, man, Helen, man, Esther The remaining woman must be Anna, and combining this with the first statement, we arrive at the following situation:Helen's husband, Anna, man, Helen, Victor, Esther Because of the third statement, Jim and Roger can be placed in only one way, and we now know the complete order:Helen's husband Roger, Anna, Jim, Helen, Victor, Esther Conclusion: the name of Helen's husband is Roger

9. In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily. After how many days will half of the pool be covered by the water-lily?

Because the water-lily doubles its size every day and the complete pool is covered after 20 days, half of the pool will be covered one day before that, after 19 days. Conclusion: After 19 days half of the pool will be covered by the water-lily .

10. On the market of Covent Garden, mrs. Smith and mrs. Jones sell apples. Mrs. Jones sells her apples for two per shilling. The apples of Mrs. Smith are a bit smaller; she sells hers for three per shilling. At a certain moment, when both ladies both have the same amount of apples left, Mrs. Smith is being called away. She asks her neighbour to take care of her goods. To make everything not too complicated, Mrs. Jones simply puts all apples to one big pile, and starts selling them for two shilling per five apples. When Mrs. Smith returns the next day, all apples have been sold. But when they start dividing the money, there appears to be a shortage of seven shilling. Supposing they divide the amount equally, how much does mrs. Jones lose with this deal?

The big pile of apples contains the same amount of large apples of half a shilling each (from mrs. Jones), as smaller apples of one third shilling each (from mrs. Smith). The average price is therefore (1/2 + 1/3)/2 = 5/12 shilling. But the apples were sold for 2/5 shilling each (5 apples for 2 shilling). Or: 25/60 and 24/60 shilling respectively. This means that per sold apple there is a shortage of 1/60 shilling. The total shortage is 7 shilling, so the ladies together started out with 420 apples. These are worth 2/5 ?420 = 168 shilling, or with equal division, 84 shilling for each. If Mrs. Jones would have sold her apples herself, she would have received 105 shilling. Conclusion: Mrs. Jones loses 21 shilling in this deal..

11. There are 4 cars . They all are coming from different directions. They have to cross through one square.They all arrive at the same time. Nobody stops . still there is no clash .
note : They all are driving at a speed if 100 km/hr.
options are:
1) all cars take left
2) all cars turn right
3) two cars turn left and two turn right.
tell me the answer with reason.

All cars turn left or right.

OR

All the cars turn through right..so that the cars will not clash with each other..since all cars are coming in the same speed there is a possible of clashing each other..but when they all turns to the same direction there may be chances to avoid the clash between the cars..

14. There are 12 balls looks identically equal. But one of them has weight different(more or less) from other. How to find that dissimilar ball with minimum balances?

Firstly divide the 12balls into three groups of 4balls numbered 1,2,3

Weigh group1(g1) against group2(g2), g2 vs g3, g3 vs g1.

One of these would be equal. Note that the other group will have the ball we are in search of. Suppose take it as g2.

Now take a ball from either g1 or g3 and weigh the 4balls against g2.

Now, which ever weighs more or less than the ball from g1 or g2.

15. In the Tour de France, what is the position of a rider, after he passes the second placed rider?

second
Because he across second position person.So he get second position.

16. You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters. How can you get just 4 liters of water using only these two jugs?

► Fill 3 liter jug n store it in a bucket.
► Again Fill 3 liter jug n store dat water in 5 liter jug.
► Again Fill 3 liter jug n store dat water till 5 liter jug gets full.
► u will get 1 liter water in dat 3 liter jug cuz u filled 5 liter jug by 3 liter jug twice i.e 3x2.
► store the remaining 1 liter into the bucket where v stored 3 liter. u will get 4 liter water now i.e 3+1

17. If 12 distinct points are placed on the circumference of a circle and all the chords connecting these points are drawn. What is the largest number of points of intersection for these chords?

So we r starting with
4 points no of intersection-1
5 " " -3
6 " " " -6
continuing and by induction we have 28 intersection with 12 points

18. 361 -> 22
121 -> 14
81 -> 12
25 -> X

What is the value of X?

Because 19*19=361 and 19+3=22.
11*11=121 and 11+3=14.
9*9=81 and 9+3=12.
5*5=25 and 5+3=8.

19. Here is a sequence of numbers: 1 11 21 1211 111221 It seems to be a strange sequence, but yet there is a system behind it... What is the next term in this sequence?

1 11 21 1211 111221 next element (2211111112)

lets see how ....

First we will ignore 1 and 11

taking 11 and 21 ... keep 11 at last = __11 and then reverse 21 as 12 and keep first we will get 1211.

moving further pick last 2 number as 21 and 1211 ...... follow same procedure keep first number in last = ....21 and now 1211 will change to 1112 ...... and keep in front 111221

next number will be

taking 1112 and 111221 as previous 2 number

......1112
2211111112 (answer) next in the sequence

20. Greengrocer C. Carrot wants to expose his oranges neatly for sale. Doing this he discovers that one orange is left over when he places them in groups of three. The same happens if he tries to place them in groups of 5, 7, or 9 oranges. Only when he makes groups of 11 oranges, it fits exactly. How many oranges does the greengrocer have at least?

Assume the number of oranges is A. Then A-1 is divisible by 3, 5, 7 and 9. So, A-1 is a multiple of 5?? = 315 (note: 9 is also a multiple of 3, so 3 must not be included!). We are looking for a value of N for which holds that 315? + 1 is divisible by 11. After some trying it turns out that N = 3. This means that the greengrocer has 946 oranges..

21. On a sunny morning, a greengrocer places 200 kilograms of cucumbers in cases in front of his shop. At that moment, the cucumbers are 99% water. In the afternoon, it turns out that it is the hottest day of the year, and as a result, the cucumbers dry out a little bit. At the end of the day, the greengrocer has not sold a single cucumber, and the cucumbers are only 98% water. How many kilograms of cucumbers has the greengrocer left at the end of the day?

In the morning, the 200 kilograms of cucumbers are 99% water. So the non-water part of the cucumbers has a mass of 2 kilograms. At the end of the day, the cucumbers are 98% water. The remaining 2% is still the 2 kilograms of non-water material (which does not change when the water evaporates). If 2% equals 2 kilograms, then 100% equals 100 kilograms. So, the greengrocer has 100 kilograms of cucumbers left at the end of the day..

22. On a nice summer day two tourists visit the Dutch city of Gouda. During their tour through the center they spot a cosy terrace. They decide to have a drink and, as an appetizer, a portion of hot "bitterballs" (bitterballs are a Dutch delicacy, similar to croquettes). The waiter tells them that the bitterballs can be served in portions of 6, 9, or 20. What is the largest number of bitterballs that cannot be ordered in these portions?

Every natural number is member of one of the following six series:
0, 6, 12, 18, ...
1, 7, 13, 19, ...
2, 8, 14, 20, ...
3, 9, 15, 21, ...
4, 10, 16, 22, ...
5, 11, 17, 23, ...
If for a number in one of these series holds that it can be made using the numbers 6, 9, and 20, then this also holds for all subsequent numbers in the series (by adding a multiple of 6). To find out what the largest number is that cannot be made using the numbers 6, 9, and 20, we therefore only need to know, for every series, what the smallest number is that can be made in that way. In the series 0, 6, 12, 18, . the smallest number that can be made is 0 so there is no number that cannot be made.In the series 1, 7, 13, 19, ... the smallest number that can be made is 49 (20+20+9) so 43 is the largest number that cannot be made.
In the series 2, 8, 14, 20, ... the smallest number that can be made is 20 so 14 is the largest number that cannot be made.In the series 3, 9, 15, 21, ... the smallest number that can be made is 9 so 3 is the largest number that cannot be made.In the series 4, 10, 16, 22, . the smallest number that can be made is 40 (20+20) so 34 is the largest number that cannot be made.In the series 5, 11, 17, 23, ... the smallest number that can be made is 29 (20+9) so 23 is the largest number that cannot be made.Therefore, 43 is the largest number that cannot be made using the numbers 6, 9, and 20

24. You are given 8 identical balls .... but one of them is slightly heavier than the rest.... given a old scale (not electronic one) and only two trials to weigh ... can u spot the odd one out?

Take six balls 3 on each side and weigh. the weighter ball is not there then put the other two in scale and u can find. or else take the balls from the weighter side of the scale and take two from them and put in the scale. if that two are equal the the ball in your hand is the weightest one.