Fewest Cut

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?


 

Answer:

Only 2 cuts!

Day One: You make your first cut at the 1/7th mark and give that to the worker.
Day Two: You cut 2/7ths and pay that to the worker and receive the original 1/7th in change.
Day three: You give the worker the 1/7th you received as change on the previous day.
Day four: You give the worker 4/7ths and he returns his 1/7th cut and his 2/7th cut as change.
Day Five: You give the worker back the 1/7th cut of gold.
Day Six: You give the worker the 2/7th cut and receive the 1/7th cut back in change.
Day Seven: You pay the worker his final 1/7th.

Sum of first n odd numbers

Mr. John Roosevelt asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Gabriel ran to him and said, 'The sum is 2,500.' Ms. John Roosevelt thought, 'Lucky guess,' and gave him the task of finding the sum of the first 75 odd numbers. Within 20 seconds, Gabriel was back with the correct answer.

How does Gabriel find the sum so quickly and what is the answer?


 

Answer:
 

The following pattern holds:

The sum is equal to n * n, when n is the number of consecutive odd numbers, starting with 1.

For example, the sum of the first 3 odd numbers (1+3+5) is equal to 3 * 3, or 9. The sum of the first 4 odd numbers (1+3+5+7) is equal to 4 * 4, or 16. The sum of the first 5 odd numbers is equal to 5 * 5, or 25; and so on.

 

 

 

Friday The 13

Many people would think Friday the 13th will be an unlucky day. Is it possible that there is no Friday on 13th through the whole year? How many Fridays at 13th can we have in a year at most? Can you calculate it out?
 

Answer:

We can calculate out how many days there will be for the 13th on each month if we count from the beginning of the year (January 1). Then we divide total days by 7 to get the remainders. We also need to consider the leap year. Through the whole year we had all kinds of remainders, from 0 to 6. The minimum of occurence for all the unique remainders was 1. It means that we have at least one Friday on 13th. In a regular year, the best chance you can get 3 Fridays on 13th, which are in February, March and December because the remainders of these 3 months are 2. In a leap year, the best chance you also can get 3 Fridays on 13th, which are in January, April and July because the remainders of these 3 months are 6.

 

A Funny Riddle (for fun)

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?







Answer:

The man is a of short stature. He can't reach the upper elevator buttons, but can push is with his umbrella on a rainy day.

Three Light Switches

Outside a room there are three light switches. One of switch is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?


 

Answer:

Set the first switches on for abt 10min, and then switch on the second switch and then enter the room.
Three cases are possible:

1.Bulb is on => second switch is the answer.
2.Bulb is off and on touching bulb , you will find bulb to be warm
=> 1st switch is the answer.
3.Bulb is off and on touching second bulb , you will find bulb to be normal(not warm)
=> 3rd bulb is the answer.

Secret Code

A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were:

The fifth number plus the third number equals fourteen.

The fourth number is one more than the second number.

The first number is one less than twice the second number.

The second number plus the third number equals ten.

The sum of all five numbers is 30.

What were the five numbers and in what order?

 

Answer:

7, 4, 6, 5, 8

7+2+5 = ?

5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
THEN ;
7+2+5 =

Answer:

143547
(7*2 , 7*5 , 7*2 + 7*5 -2)
 

9 coins

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

Answer:

The answer is 2. First, divide the coins into 3 equal piles. Place a pile on each side of the scale, leaving the remaining pile of 3 coins off the scale. If the scale does not tip, you know that the 6 coins on the scale are legitimate, and the counterfeit is in the pile in front of you. If the scale does tip, you know the counterfeit is in the pile on the side of the scale that raised up. Either way, put the 6 legitimate coins aside. Having only 3 coins left, put a coin on each side of the scale, leaving the third in front of you. The same process of elimination will find the counterfeit coin.

The highest chance of survival

Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?

 

Answer:

He should shoot at the ground.

If Mr. Black shoots the ground, it is Mr. Gray's turn. Mr. Gray would rather shoot at Mr. White than Mr. Black, because he is better. If Mr. Gray kills Mr. White, it is just Mr. Black and Mr. Gray left, giving Mr. Black a fair chance of winning. If Mr. Gray does not kill Mr. White, it is Mr. White's turn. He would rather shoot at Mr. Gray and will definitely kill him. Even though it is now Mr. Black against Mr. White, Mr. Black has a better chance of winning than before.

Entangled Figures

Examine the image below; then determine which three of the nine figures below it are combined to form the image.

 

 

 

Answer:

Figures 2, 4, and 6 are part of the image.

Missing Letters

Fill in the missing letters in the box below.

Answer:

TET
They are the initial letters of the first 12 numbers.

Ferrying Soldiers

A detachment of 25 soldiers must cross a wide and deep river with no bridge in sight. They notice two 12-year-old boys playing in a rowboat by the shore. The boat is so tiny, however, that it can only hold two boys or one soldier. How can the soldiers get across the river and leave the boys in joint possession of the boat? How many times does the boat pass from shore to shore in your algorithm?

Answer:

First, the two boys take the boat to the other side, after which one of them returns with the boat. Then a soldier takes the boat to the other side and stays there while the other boy returns the boat. These four trips reduce the problem size—measured by the number of soldiers to be ferried—by 1. Thus, if this fourtrip procedure is repeated the total of 25 times, the problem will be solved after the total of 100 trips. (Of course, for the general instance of n soldiers, 4n trips will need to be made.)

Arrange Symbols!

Complete the grid using only the five symbols shown in the top line so that the same two symbols do not appear in any horizontal, vertical or diagonal line.




Arrange Symbols

Answer:

 

Form a Cube

Can you tell, just by stu-dying them, how many of the following can be fold-ed to form a cube?




Form a Cube

 

Answer:

A, B and D can be folded to form a cube

Find four figures in twenty seconds!

In the following figure can you find which four figures are identical in twenty seconds?

 

Answer:

H, I, O, and Q

A Wolf, a Goat, and a Cabbage

A man finds himself on a riverbank with a wolf, a goat, and a head of cabbage. He needs to transport all three to the other side of the river in his boat. However, the boat has room for only the man himself and one other item (either the wolf, the goat, or the cabbage). In his absence, the wolf would eat the goat, and the goat would eat the cabbage. Show how the man can get all these “passengers” to the other side.

 

Answer:

Let M, w, g, and c stand for the man (with the boat, which is always on the same bank of the river as the man), wolf, goat, and cabbage head, respectively. The following figure depicts two sequences of trips that solve the problem.

 

Synonyms & Antonyms

Select two words that are synonyms, plus an antonym of these two synonyms, from the list of words below.

choke, force, thrive, toil, wither, burgeon, strive

 

Answer:

Synonyms: thrive, burgeon
Antonym: wither

Find identical figures in thirty seconds!

In the following figure, can you find which four figures are identical in thirty seconds?

Answer:

C, F, M, and P

Which set of symbols should replace the question marks?

Answer:

A; each line moves 45° clockwise from top to bottom.

Word Squares

Each letter in this puzzle represents a different number from zero to nine. It is your challenge to switch these letters back to numbers in such a way that each horizontal, vertical, and diagonal row of three words totals the same number. Your total for this puzzle is 1446.

 

Answer:

 

Four Identical Figures

In the following figure can you find which four figures are identical in thirty seconds?

Answer:

D, F, N, and S

Sequence

There is a logical way to get from the top left-hand square to the bottom right by moving from square to square horizontally, vertically or diagonally and visiting every square once only. What is it?

Answer:

Peter or Paul

Peter and Paul are twin brothers. One of them (we don't know which) always lies. The other one always tells the truth. I ask one of them: "Is Paul the one that lies?" "Yes," he answers. Did I speak to Peter or Paul?

Answer:

I spoke to Peter. If a person always lies or alternately, always tells the truth, he cannot admit that he is lying (if this person were a liar, he would be telling the truth, and if this person were honest, he would be lying). Therefore, Paul could not have answered my question. Peter could answer about Paul without contradicting himself. What we don't know is who the liar is.