Find Next Three Numbers

Puzzle:

Find next three numbers in the given series...

1 2 3 2 1 2 3 4 2 1 2 3 4 3 2 ? ? ?

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Solution:

The next three numbers are 3, 4 and 5.

The pattern is - the number of letters in the Roman numeral representation of the numbers i.e. number of letters in I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII, XIII, XIV, XV, ..... Hence, the next numbers in the given series are 3(XVI), 4(XVII), 5(XVIII), 3(XIX), 2(XX), 3(XXI), 4(XXII), 5(XXIII), 4(XXIV), 3(XXV), etc...

Seating Arrangement

Puzzle:

Mrs. F has invited several wives of delegates to the United Nations for an informal luncheon. She plans to seat her 9 guests ina row such that each lady will be able to converse with the person directly to her left and right. She has prepared the following list.

Mrs. F speaks English only.
Mrs. G speaks English and French.
Mrs. H speaks English and Russian.
Mrs. J speaks Russian only.
Mrs. K speaks English only.
Mrs. L speaks French only.
Mrs. M speaks French and German.
Mrs. N speaks English and German.
Mrs. O speaks English only.

How many distinct seating arrangements are possible? Give all possible seating arrangements.

Note that ABCD and DCBA are the same.

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Solution:

126 distinct seating arrangements are possible.

Mrs. J and Mrs. H must be together and Mrs. J must be at the end as Mrs. J speaks only Russian and Mrs. H is the only other Russian speaker.

Mrs. L speaks only French and there are two others - Mrs. G and Mrs. M - who speak French. Here there are 2 cases.
• CASE A : Mrs. L is at the other end
If Mrs. L is at the other end, either Mrs. G or Mrs. M must seat next to her.
o CASE AA : Mrs. G seats next to Mrs. L
Then, Mrs. M must seat next to Mrs. G and Mrs. N must seat next to Mrs. M. This is because Mrs. M speaks French and German, and Mrs. N is the only other German speaker. Thus, the possible seating arrangement is JHxxxNMGL, where x is the English speakers. Mrs. F, Mrs. K and Mrs. O can be arranged in remaining 3 positions in 3! different ways i.e. 6 ways.
o CASE AB : Mrs. M seats next to Mrs. L
If so, then either Mrs. N or Mrs. G must seat next to Mrs. M
? CASE ABA : Mrs. N seats next to Mrs. M
Thus, the possible seating arrangement is JHxxxxNML, where x is the English speakers. Mrs. F, Mrs. G, Mrs. K and Mrs. O can be arranged in remaining 4 positions in 4! different ways i.e. 24 ways.
? CASE ABB : Mrs. G seats next to Mrs. M
Thus, the possible seating arrangement is JHxxxxGML, where x is the English speakers. Mrs. F, Mrs. K, Mrs. N and Mrs. O can be arranged in remaining 4 positions in 4! different ways i.e. 24 ways.

• CASE B : Mrs. L does not seat at the end
It means that Mrs. G, Mrs. L and Mrs. M must seat together. Also, Mrs. L must seat between Mrs. G and Mrs. M.

o CASE BA : Mrs. G seats left and Mrs. M seats right to Mrs. L i.e. GLM

? CASE BAA : GLM is at the other end
Thus, the possible seating arrangement is JHxxxxGLM, where x is the English speakers. Mrs. F, Mrs. K, Mrs. N and Mrs. O can be arranged in remaining 4 positions in 4! different ways i.e. 24 ways.
? CASE BAB : GLM is not at the other end
Then Mrs. N must seat next to Mrs. M. Now, we have a group of four GLMN where Mrs. G and Mrs. N speak English. Thus, the possible seating arrangement is JHxxxX, where x is the individual English speakers and X is the group of four females with English speakers at the both ends. Thus, there are 4! different ways i.e. 24 ways.

o CASE BB : Mrs. M seats left and Mrs. G seats right to Mrs. L i.e. MLG
Then, Mrs. N must seat next to Mrs. M. Now, we have a group of four NMLG where Mrs. G and Mrs. N speak English. Thus, the possible seating arrangement is JHxxxX, where x is the individual English speakers and X is the group of four females with English speakers at the both ends. Thus, there are 4! different ways i.e. 24 ways.
Thus, total different possible seating arrangements are :
= 6 (case AA) + 24 (case ABA) + 24 (case ABB) + 24 (case BAA) + 24 (case BAB) + 24 (case BB)
= 126 seating arrangements

Thus, 126 distinct seating arrangements are poosible.

N secret agents

Puzzle:

There are N secret agents each know a different piece of secret information. They can telephone each other and exchange all the information they know. After the telephone call, they both know anything that either of them knew before the call. What are the minimum number of telephone calls needed so that all of the them know everything?

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Solution:

(2N - 3) telephone calls, for N = 2,3
(2N - 4) telephone calls, for N > 3

Divide the N secret agents into two groups. If N is odd, one group will contain one extra agent.

Consider first group: agent 1 will call up agent 2, agent 2 will call up agent 3 and so on. Similarly in second group, agent 1 will call up agent 2, agent 2 will call up agent 3 and so on. After (N - 2) calls, two agents in each the group will know anything that anyone knew in his group, say they are Y1 & Y2 from group 1 and Z1 & Z2 from group 2.

Now, Y1 will call up Z1 and Y2 will call up Z2. Hence, in next two calls total of 4 agents will know everything.

Now (N - 4) telephone calls are required for remaining (N - 4) secret agents.

Total telephone calls require are
= (N - 2) + 2 + (N - 4)
= 2N - 4

Travel

Puzzle:

A person travels on a cycle from home to church on a straight road with wind against him. He took 4 hours to reach there. On the way back to the home, he took 3 hours to reach as wind was in the same direction. If there is no wind, how much time does he take to travel from home to church?

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Solution:

3 hours 25 minutes 42 seconds

Let distance between home and church is D. A person took 4 hours to reach church. So speed while travelling towards church is D/4. Similarly, he took 3 hours to reach home. So speed while coming back is D/3. There is a speed difference of 7*D/12, which is the wind helping person in 1 direction, & slowing him in the other direction. Average the 2 speeds, & you have the speed that person can travel in no wind, which is 7*D/24. Hence, person will take D / (7*D/24) hours to travel distance D which is 24/7 hours.

Age

Puzzle:

Sam and Mala have a conversation.

• Sam says I am certainly not over 40
• Mala says I am 38 and you are atleast 5 years older than me
• Now Sam says you are atleast 39

All the statements by the two are false. How old are they really?

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Solution:

Sam is 41 and Mala is 37.

Let's invert the teaser and read it like this :
• Sam says I am certainly over 40
• Mala says I am not 38 and you are atmost 4 years older than me
• Now Sam says you are atmost 38
From first statement it is clear that Sam is over 40. Also, from next 2 statements it is clear that Mala is less then 38. Hence the possibilities are :
Sam = 41, 42, 43, 44, 45, ......
Mala = 37, 36, 35, 34, 33, ......

It also says that the difference between their age is maximum 4 years. Hence, there is only one possible pair i.e. 41 and 37, all other combination have differences more then 4.

Hence the answer - Sam is 41 and Mala is 37.

Robbery

Puzzle:

After a local shop robbery, four suspects were being interviewed. Below is a summary of their statements. Police know that each of them told the truth in one of the statements and lied in the other. From this information can you tell who committed the crime?

Anil said:
It wasn't Deepak
It wasn't Bhaskar
Bhaskar said:
It wasn't Charan
It was Deepak
Charan said:
It was Anil
It wasn't Depak
Deepak said:
It was Charan
It wasn't Anil

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Solution:

Bhaskar robbed the store.

The original number

Puzzle:

I bought a car with a peculiar 5 digit numbered licence plate which on reversing could still be read. On reversing, its value is increased by 78633. Whats the original number if all digits are different?

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Solution:

Only 0 1 6 8 and 9 can be read upside down. So on rearranging these digits we get the answer as 10968.

A Farmer

Puzzle:

A farmer needs 8 gallons of water. He has only three unmared buckets, two 6 gallon and one 11 gallon bucket. How can he collect 8 gallons of water using three unmarked buckets? Provide solution with minimal water wastage.

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Solution:

Here is the solution with 10 gallon water wastage.
OPERATIONS 6 6 11
Fill 6 gallon bucket with water 6 0 0
Empty 6 gallon bucket into 11 gallon bucket 0 0 6
Fill 6 gallon bucket with water 6 0 6
Fill 11 gallon bucket to full using filled 6 gallon bucket. This will leave 1 gallon water in 6 gallon bucket 1 0 11
Empty 11 gallon bucket into second 6 gallon bucket. 1 6 5
Empty 11 gallon bucket - wastage of 5 gallon water 1 6 0
Empty second 6 gallon bucket into 11 gallon bucket 1 0 6
Fill seccond 6 gallon bucket with water 1 6 6
Fill 11 gallon bucket to full using filled second 6 gallon bucket. This will leave 1 gallon water in second 6 gallon bucket 1 1 11
Fill first 6 gallon bucket with 1 gallon water which is in second 6 gallon bucket 2 0 11
Empty 11 gallon bucket into second 6 gallon bucket. 2 6 5
Empty 11 gallon bucket - wastage of 5 gallon water 2 6 0
Fill 11 gallon bucket with water in both the 6 gallon buckets 0 0 11

Movie

Puzzle:

Last Saturday Milan went for the late night show and came late. In the morning family members asked him which movie did he see. He gave different answers to everyone.

• He told to his father that he had gone to see MONEY.
• According to his mom, he saw either JOHNY or BABLU.
• His elder brother came to know that he saw BHABI.
• To his sister, he told ROBOT.
• And his grandpa heard that he saw BUNNY.
  

Thus, Milan gave six movie names, all five letter words. But he saw some other movie with five letter word. Moreover, each of the six movie names mentioned above has exactly two letters common with the movie he saw. (with the same positions)

Can you tell which movie did Milan see?

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Solution:

Milan saw BOBBY.

The six movie names are - MONEY, JOHNY, BABLU, BHABI, ROBOT and BUNNY.

Compare MONEY and JOHNY. They have O common at the second place and Y common at the fifth place. Also, they can't have two different letters each, common with the required movie as the letters in remaining three places are all different. Thus, the required movie must have either O at the second place or Y at the fifth place or both.

Similarly, comparing JOHNY and BUNNY - the required movie must have either N at the fourth place or Y at the fifth place or both. Also, comparing MONEY and BUNNY - the required movie must have either N at the third place or Y at the fifth place or both.

From the above 3 deduction, either Y is at fifth place or O is at the second place and N is at the third & fourth place. The later combination is not possible as BABLU, BHABI & ROBOT will need at least 3 other letters which makes the required movie 6 letter long. Hence, the required movie must have Y at the fifth place.

Now Y is not there in BABLU and BHABI at the fifth place and they have only B common at the first place. Hence, B must be the first letter.

As B is at the first place and Y is at the fifth place and every movie has exactly 2 letters common with the required movie. From BUNNY, the required movie do not have U at the second place and N at the third and fourth place. Now looking at JOHNY and MONEY, they must have O common at the second place.

Using the same kind of arguments for BABLU, BHABI and ROBOT, we can conclude that Milan saw BOBBY.

Doctor & Engineer

Puzzle:

One of Mr. Bajaj, his wife, their son and Mr. Bajaj’s mother is an Engineer and another is a Doctor.

• If the Doctor is a male, then the Engineer is a male.
• If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives.
• If the Engineer is a female, then she and the Doctor are blood relatives.
  

Can you tell who is the Doctor and the Engineer?

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Solution:

Mr. Bajaj is the Engineer and either his wife or his son is the Doctor.

Mr. Bajaj's wife and mother are not blood relatives. So from 3, if the Engineer is a female, the Doctor is a male. But from 1, if the Doctor is a male, then the Engineer is a male. Thus, there is a contradiction, if the Engineer is a female. Hence, either Mr. Bajaj or his son is the Engineer.

Mr. Bajaj's son is the youngest of all four and is blood relative of each of them. So from 2, Mr. Bajaj's son is not the Engineer. Hence, Mr. Bajaj is the Engineer.

Now from 2, Mr. Bajaj's mother cannot be the Doctor. So the Doctor is either his wife or his son . It is not possible to determine anything further.

Number Cycles

Puzzle:

Find a cycle of five 4-digit numbers such that the last 2 digits of each number are equal to the first 2 digits of the next number in the cycle. Each of the 5 numbers must be exactly one of the following types (with each of the 5 types being represented exactly once): Square, Cube, Triangular, Prime, Fibonacci. The solution is unique.

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Solution:

8117, 1728, 2850, 5041, 4181 (Prime, Cube, Triangular, Square, Fibonacci)

Six 9's make 100

Puzzle:

Can you just use only +, -, *, / to make six 9’s equal 100? Do you think this is too easy. There are at least 6 solutions.

9 ..9 ..9 ..9 ..9 ..9 = 100

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Solution:

9 * 9 + 9 + 9 + 9/9 = 100
99 + 99 / 99 = 100
(99 + 9/9) * 9 / 9 = 100
(99 + 9/9) + 9 - 9 = 100
(9 + 9/9) * (9 + 9/9) = 100
(999 - 99) / 9 = 100
99 / 9 * 9 + 9 / 9 = 100
(99 + 9/9) / (9 / 9) = 100

No Intersection

Puzzle:

Within the rectangle, draw a line to connect from circle 1 to the other circle 1, then draw a line from circle 2 to the other circle 2, and so on. There should not be any intersections.

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Solution:

Draw a line (line A) from 3 to 3 and draw another line (line B) from 4 to 4 first. Since there is no intersection for line A and B, there must be a gap between lines. Draw a line from 1 to 1 to go through the gap. Draw another line from 2 to 2 to go through the gap again.

Mixed Nuts

Puzzle:

A mixed packet of nuts contains 1 pound of walnuts and 2 pounds of Brazil nuts. It costs exactly $2. A packet containing 4 pounds of filberts and 1 pound of walnuts costs $3. And for only $1.50, you can buy a mixed packet of 3 pounds of almonds, 1 pound of walnuts, and 1 pound of filberts. How much should you pay for a mixture of 1 pound of each of the four kinds?

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Solution:

A mixture of 1 pound of each of the four kinds costs $2

It is not possible to work out the cost per pound of each of the different nuts. However, the cost of various combinations can be worked out to get one pound of each of the four kind of nuts.

5 Digit Number

Puzzle:

Can you find a five digit number which has no zeros no digit is repeated, where:

• The first digit is a prime number.
• The second digit is the fifth digit minus the first digit.
• The third digit is twice the first digit.
• The fourth digit is the third digit plus three.
• The fifth digit is the difference between the first digit and the fourth digit.
  

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Solution:

The five digit number is 23475.

Pharmacy

Puzzle:

The pharmacy has an old scale which has only two measuring weights 30 grams and 5 grams. How can you divide 300 grams of powder medicine into 3 groups, one 150 grams, one 100 and the other 50 grams. You can only weigh 3 times.

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Solution:

First, we use 300 grams of medicine and 30 gram weight to split 300 medicine into 165 and 135 grams.

Then we use 165 grams of medicine and 30 + 5 gram weights to separate 165 grams into 100 and 65 grams.

Then we further separate the 65 grams into 50 grams and 15 grams.

Finally, Combine 135 and 15 grams to 150 grams.

Plus & Minus

Puzzle:

Below is an equation that isn't correct yet. By adding a number of plus signs and minus signs between the ciphers on the left side (without changes the order of the ciphers), the equation can be made correct.

123456789 = 100

How many different ways can you find that makes the equation correct?

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Solution:

There are 12 different ways:

123+45-67+8-9=100
123+4-5+67-89=100
123-45-67+89=100
123-4-5-6-7+8-9=100
12+3+4+5-6-7+89=100
12+3-4+5+67+8+9=100
12-3-4+5-6+7+89=100
1+23-4+56+7+8+9=100
1+23-4+5+6+78-9=100
1+2+34-5+67-8+9=100
1+2+3-4+5+6+78+9=100
-1+2-3+4+5+6+78+9=100

The Cucumber

Puzzle:

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?

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Solution:

The greengrocer has 100 kilograms of cucumbers 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.

Sweets

Puzzle:

A kind old gentleman decided to give 12 sweets to each of the girls in his town and 8 sweets to each of the boys. Of the 612 children in his town, only half the girls and three quarters of the boys were allowed to take the sweets. How many sweets did the kind old gentleman have to buy?

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Solution:

3,672 Sweets

Escalator

Math Puzzle:

You walk upwards on an escalator, with a speed of 1 step per second. After 50 steps you are at the end. You turn around and run downwards with a speed of 5 steps per second. After 125 steps you are back at the beginning of the escalator. How many steps do you need if the escalator stands still?

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Solution:

100 Steps.

Let v be the speed of the escalator, in steps per second. Let L be the number of steps that you need to take when the escalator stands still. Upwards (along with the escalator), you walk 1 step per second. You need 50 steps, so that takes 50 seconds. This gives: L - 50 × v = 50. Downwards (against the direction of the escalator), you walk 5 steps per second. You need 125 steps, so that takes 25 seconds. This gives: L + 25 × v = 125. From the two equations follows: L = 100, v = 1. When the escalator stands still, you need 100 steps.

Secret Code

Puzzle:

The only way to get a free drink in this bar, is to prove to the barman that you are a friend of his boss. Here's how its done. You go to the barman, he tells you a number and you tell him the "countersign" number. If your answer is correct you get your drink. There's this mathematician who thought that there can't be a standard list of numbers and countersign numbers. There must be an algorithm that provides the answer from the number given by the barman. So he joins a party of three men who ARE friends of the boss and walks with them to the bar hopping to understand the algorithm from the three answers. HERE'S WHAT HE HEARD: The barman says "6" to the first man, he says "3" and got his drink. The barman said "12" to the second man, who replied "6" and got his drink. The barman said "14" to the third man and he answered "8" (!) and got his drink. Now its the mathematicians turn. "20", said the barman. What is the counter sign?

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Solution:

Six

You count the number of letters in the word. Twenty has 6 letters so the mathematician should say "six".

Sack of Apples

Puzzle:

A man had to pack a sack of apples into packets but as each packet had to have exactly the same number of apples he was having difficulty. If he packed 10 apples per packet, one packet only had 9. If he packed 9 apples per packet, one packet only had 8. If he packed 8 apples per packet, one packet only had 7. If he packed 7 apples per packet, one packet only had 6. And so on down to 2 apples. How many apples did he start with?

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Solution:

2519 apples.

The solution for the answer is the LCM (Lowest Common Multiple) of 10,9,8,7,6,5,4,3,2,1 minus 1. LCM would give the least number which is divisible by all of these number and subtracting one would give us the number of apples which were initially there.

Fruit Stall

Puzzle:

At a fruit stall in Puzzle land, an Apple costs Rs.17, an Orange costs Rs.21, and a Pear costs Rs.14. What is the cost of a mango?

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Solution:

Cost of Mango is Rs.17

Each vowel cost Rs.4 and each consonants cost Rs.3

Positive Integer

Puzzle:

Find a positive integer (base 10) which has the following four properties:

• Each of the 10 digits (0 to 9) appears exactly once in the number.
• For each pair of digits whose sum is 9, the number of other digits positioned strictly between the pair is equal to the smaller digit of the pair.
• The sum of each pair of digits positioned at the same distance from opposite ends of the number is a prime number.
• The difference between any 2 adjacent digits is greater than 1.
  

The solution is unique. Find the Number.

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Solution:

The number is 5831746290

Time

Puzzle:

I was having trouble sleeping last night and I tossed and turned well into the night. Our local town hall has a clock which strikes on the hour and also strikes just once on the half hour. During one of my more awake moments I heard the clock strike once, but I could not tell what time it was. Half an hour later it struck once again, but I still could not tell what time it was. Finally, half an hour later it struck once again and I knew what the time was. What time was it?

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Solution:

1.30 in the morning. The initial single strike was at 12.30.

Find Next Number

Puzzle:

Find next number in the series...

1/1...3/2 ...7/5...17/12...41/29...?

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Solution:

Next number in the series is 99/70

The successive term for a/b is formed as (a + 2b) / (a + b).

Birds and Trees

Puzzle:

There is a forest with trees. On each and every tree in the forest, exactly the same number of birds are sitting on it (ex. "There are 5 trees and each tree has 5 birds on it"). The birds in the forest is a given number between 200 and 300. How many trees are in our forest(such that there is no other combination of trees and birds to acquire the same product)?

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Solution:

There are 289 birds and 17 trees in the forest (with 17 birds per tree).

We are looking for a number whose square is between 200 and 300. The candidates are 15, 16 and 17. It can't be 15, because 15*15 = 45*5 = 5*45, so again NO unique answer on the number of trees. Similarly it can't be 16, because 16*16 = 8*32 = 32*8. But 17*17 = 289 and there isn't any other pair of numbers whose product is 289. So, for 289 birds there can be only 17 trees in the forest (with 17 birds per tree) and this is the only unique answer available.

5 Consecutive Integers

Puzzle:

In the equation shown below, A, B, C, D, and E are 5 consecutive positive integers. What are they?

A*A + B*B + C*C = D*D + E*E

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Solution:

A=10, B=11, C=12, D=13, E=14.
10x10 + 11x11 + 12x12 = 13x13 + 14x14

Gold in a Box

Puzzle:

We have two closed boxes with a label on each one. Label A on box A: "The label on box B is true and the gold is in box A" Label B on box B: "The label on box A is false and the gold is in box A" We don't know if the labels (one or both of them) are true or false. Knowing FOR SURE that the gold is in box A or in box B, where's the gold?

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Solution:

The Gold is in box B.

Lets assume that label A is true. This means that label B is also true and the gold is in box A. In this case, the label A is false. This CAN'T be, because we assumed that the label A is true. Thus, our first assumption is invalid. So now we know that label A is lying. This leads us to two cases: (1) The label B is false. (2) The gold is in box B (now that we know that it cant be in box A). If (1) was true, then the gold is in box B or label A is true - which can't be because we know that label A is lying. So in BOTH CASES the gold IS IN BOX B

MEATS

Puzzle:

The MEATS is the result of multiplication. Each letter stands for a distinct digit. What is the 'MEATS'?

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Solution:

MEATS, the result of multiplication is 39784

4973 x 8 = 39784

Bathtub

Puzzle:

You want to fill a bathtub by running water from both the hot and cold taps. The hot tap takes 6 minutes to fill the tub alone and the cold tap takes 4 minutes to fill alone. So you turn them both on at the same time but you are unaware that you left the plug out. The plug empties the tub in 12 minutes. How long will it take to fill the tub?

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Solution:

3 minutes

Solve this by:
(1/6 + 1/4 - 1/12) ^ (-1)
= (1/3)^(-1) = 3